KM086 - Food Processor KENWOOD - Free user manual and instructions

Product type	Food processor
Brand	KENWOOD
Model	KM086
Power supply	Mains, 220-240 V ~ 50/60 Hz
Power	~ 1000 W
Speeds	Variable with pulse (P)
Bowl capacity	4.5 litres (approx.)
Main functions	Beat, whip, knead, mix
Included accessories	K-beater, whisk, dough hook, spatula
Accessory outlets	2 outlets (fast, slow), juicer outlet, planetary outlet
Weight	Approx. 8 kg
Dimensions (W x D x H)	Approx. 30 x 30 x 40 cm
Bowl material	Stainless steel (optional)
Safety	Automatic shutdown in case of overload? Not specified
Care and cleaning	Clean accessories by hand; wipe the motor unit with a damp cloth
Spare parts and repairability	Accessories available (mincer, juicer, etc.); repair by Kenwood authorized service

Frequently Asked Questions - KM086 KENWOOD

How do I adjust the height of the whisk or K-beater?

Unplug the appliance, raise the head, hold the accessory and loosen the nut. Lower the head and turn the shaft to adjust the height. The accessory should almost touch the bottom of the bowl. Raise the head and tighten the nut.

Can I use the whisk for thick mixtures?

No, the whisk is only for light mixtures (eggs, cream). For thick mixtures, use the K-beater or dough hook.

What is the maximum flour capacity for bread?

For the KM086 model, the maximum flour capacity is about 2.5 kg, but check the instructions to avoid overloading the appliance.

How do I clean the food processor?

Turn off and unplug the appliance. Wash the accessories by hand (dishwasher may discolor). Wipe the motor unit with a damp cloth. Never immerse the motor unit.

What if the K-beater hits the bottom of the bowl?

Adjust the height: unplug, raise the head, loosen the nut, lower the head, turn the shaft to adjust, then tighten the nut.

Can I use multiple accessories at the same time?

No, use only one accessory at a time. Do not exceed the recommended maximum capacities.

How do I add ingredients during mixing?

You can add ingredients directly into the bowl through the hinged section of the splash guard, without removing the lid.

Where can I find additional accessories?

Contact Kenwood customer service or the store where you purchased the appliance. Accessories such as the mincer, juicer, or food mill are available.

The food processor makes an abnormal noise, what should I do?

Turn off and unplug the appliance. Check for overload or obstruction. If the problem persists, contact a Kenwood authorized repairer.

Can I use the food processor to make shortcrust pastry?

Yes, use the K-beater on speed 1 until crumbly, then add water and mix at minimum speed. Do not overmix.

USER MANUAL KM086 KENWOOD

Kenwood Chef KM200, KM300, KM400 series Major KM600, KM800 series

Kenwood

English

page 3 instructions

Congratulations on buying a Kenwood. With such a wide range of attachments available, it's more than just a mixer. It's a state-of-the-art kitchen machine. We hope you'll enjoy it. Robust. Reliable. Versatile. Kenwood.

Français

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know your Kenwood kitchen machine

safety

• Switch off and unplug before fitting or removing tools/attachments, after use and before cleaning.
• This machine is not intended for use by young children or infirm persons without supervision.
• Keep your fingers away from moving parts and fitted attachments.
• Never leave the machine on unattended.
• Never use a damaged machine. Get it checked or repaired: see 'service', page 8.
• Never use an unauthorised attachment or more than one attachment at once.
• Never exceed the maximum capacities on page 4.
• Don't let children play with this machine.
• When using an attachment, read the safety instructions that come with it.
• Only use this machine for domestic food preparation.

before using for the first time

1 Remove all packaging.
2 Wash the parts: see 'care and cleaning', page 8.

attachment outlets

know your Kenwood kitchen machine

high-speed outlet
2 citrus juicer outlet

the mixer 3 slow-speed outlet

4 tool socket
(5) mixer head
(6) outlet catch
⑦ bowl
⑧ head-lift lever
(9) on/off and speed switch
10 power unit
11 K-beater
(12)whisk
⑬ dough hook
⑭ spatula

the mixer

the mixing tools and some of their uses

K-beater • For making cakes, biscuits, pastry, icing, fillings, éclairs and mashed potato.

whisk - For eggs, cream, batters, fatless sponges, meringues, cheeses, moussees, soufflés. Don't use the whisk for heavy mixtures (eg creaming fat and sugar) - you could damage it.

dough hook For yeast mixtures.

to use your mixer

1 Turn the head-lift lever anti-clockwise ① and raise the mixer head till it locks.

to insert a tool 2 Turn till it stops ② then push.

3 Fit the bowl onto the base - press down and turn clockwise ③

4 Turn the head-lift lever anti-clockwise and lower the mixer head till it locks.

5 Select a speed, then switch on by turning the speed switch.

• Switch to pulse P for short bursts.

to remove a tool 6 Unscrew.

hints - Switch off and scrape the bowl with the spatula frequently.
- Eggs at room temperature are best for whisking.
- Before whisking egg whites, make sure there's no grease or egg yolk on the whisk or bowl.
- Use cold ingredients for pastry unless your recipe says otherwise.

points for bread making

important • Never exceed the maximum capacities below - you'll overload the machine.

• If you hear the machine labouring, switch off, remove half the dough and do each half separately.
• The ingredients mix best if you put the liquid in first.

maximum capacities

KM300, 400, 410 models

KM600, 800, 810 models

shortcrust pastry

Flour weight: 680g - 1lb 8oz

Flour weight: 910g - 2lb

stiff yeast dough

Flour weight: 1.36kg - 3lb

Flour weight: 1.5kg - 3lb 5oz

British type Total weight: 2.18kg - 4lb 13oz

Total weight: 2.4kg - 5lb 5oz

soft yeast dough

Flour weight: 1.3kg - 2lb 14oz

Flour weight: 2.6kg - 5lb 12oz

continental type

Total weight: 2.5kg - 5lb 8oz

Total weight: 5kg -11lb

fruit cake mix

Total weight: 2.72kg - 6lb

Total weight: 4.55kg - 10lb

egg whites 12

16

speeds 4

K-beater • creaming fat and sugar start on min, gradually increasing to max.

• beating eggs into creamed mixtures 4 - 'max'.
• folding in flour, fruit etc Min - 1.
• all in one cakes start on min speed, gradually increase to max.
• rubbing fat into flour min - 2.

whisk Gradually increase to 'max'.

dough hook Start on 'min', gradually increasing to 1.

troubleshooting

problem

• The whisk or K-beater knocks against the bottom of the bowl or isn't reaching the ingredients in the bottom of the bowl.
• Adjust the height. Here's how:

1 Unplug.
2 Raise the mixer head and insert the whisk or beater.
3 Hold it, then loosen the nut 1
4 Lower the mixer head.
5 Adjust the height by turning the shaft. Ideally the whisk/K-beater should be almost touching the bottom of the bowl 2
6 Raise the head, hold the whisk/K-beater and tighten the nut.

to fit and use your round/D-shaped splashguard (if supplied)

1 Raise the mixer head until it locks.
2 Fit the bowl onto the base.
3 Push the splashguard on until fully located 3. The hinged section should be positioned as shown round 4 and D-shaped 5
4 Insert required tool.
5 Lower the mixer head ensuring the splashguard follows the shape of the bowl.
- During mixing, ingredients can be added directly to the bowl via the hinged section of the splashguard.
- You do not need to remove the splashguard to change tools.
6 Remove the splashguard by raising the mixer head and sliding it down.

the attachments available

To buy an attachment not included in your pack, call your KENWOOD repairer.

attachment attachment code

flat pasta maker ① A970

additional pasta attachments A971 tagliatelle (not shown) used in conjunction A972 taglionlini with A970 A973 trenette A974 spaghetti

pasta maker ② A936 comes with 6 screens

slow speed slicer/shredder ③ A948 comes with 4 drums

super mincer ④ A950 comes with

a large sausage nozzle
b small sausage nozzle
c kebbe maker

grain mill ⑤ A941

citrus press ⑥ A995

liquidiser ⑦ 1.2 | acrylic A993A, 1.2 | glass A994A, 1.5 | stainless steel A996A
multi-mill ⑧ A938A comes with 3 glass jars and 3 lids for storage

high speed slicer/shredder ⑨ A998 comes with 3 cutting plates

optional plates a extra coarse shredder part number 639021

b rasping plate part number 639150
c standard chipper part number 639083

continuous juice extractor ⑩ A935

ice-cream maker (1) CHEF A953, MAJOR A954

potato peeler 12CHEF A934, MAJOR A952

der and sieve (3) CHEF A992. MAJOR A930

kenlyte round bowlCHEF 265026, MAJOR 412095

round splashguard a CHEF & MAJOR 444347

kenlyte D-shaped bowlCHEF 489969

D-shaped splashguard a CHEF 604349

stainless steel bowls 16 polished: CHEF 638821, MAJOR 642779

cover ⑦ CHEF 533722, MAJOR 606397

(4)

cleaning and service

care and cleaning

Always switch off and unplug before cleaning.
- A little grease may appear at outlets 2 and 3 when you first use them. This is normal - just wipe it off.

power unit Wipe with a damp cloth, then dry.

• Never use abrasives or immerse in water.
• Wash by hand, then dry thoroughly.
• If you have a stainless steel bowl, never use a wire brush, steel wool or bleach. Use vinegar to remove limescale. The stainless steel bowl may also be washed in the dishwasher.
• Keep away from heat (cooker tops, ovens, microwaves).

tools · Wash by hand, then dry thoroughly.

• Discolouration of the K beater, whisk and dough hook may occur if
  placed within a dishwasher.

splashguard Wash by hand, then dry thoroughly.

service and customer care

• If the cord is damaged it must, for safety reasons, be replaced by KENWOOD or an authorised KENWOOD repairer.

UK If you need help with:

• using your machine
• servicing or repairs (in or out of guarantee)

call KENWOOD on 023 92392333 and ask for Customer Care.

Have your model number ready - it's on the underside of the mixer.

Alternatively, contact your authorised KENWOOD repairer:

look in Yellow Pages under 'Electrical appliance repairs'.

Eire - See our advertisement in Golden Pages.

other countries Contact the shop where you bought your machine.

guarantee UK only

If your machine goes wrong within one year from the date you bought it, we will repair or replace it free of charge provided:

• you have not misused, neglected or damaged it;
• it has not been modified;
• it is not second-hand;
• it has not been used commercially;
• you have not fitted a plug incorrectly; and
• you supply your receipt to show when you bought it.

This guarantee does not affect your statutory rights.

recipes

See important points for bread making on page 4.

white bread stiff British-type dough

ingredients

1.36kg (3lb) strong plain flour
15ml (3tsp) salt
- 25g (1oz) fresh yeast; or 15 g/20ml( 1/2oz) dried yeast + 5ml (1 tsp) sugar
- 750ml (1½pts) warm water: 43^ (110^) . Use a thermometer or add 250ml (9fl oz) boiling water to 500ml (18fl oz) cold water
25g (1oz) lard

method

1 dried yeast (the type that needs reconstituting): pour the warm water into the bowl. Then add the yeast and the sugar and leave to stand for about 10 minutes until frothy.

fresh yeast: crumble into the flour.

other types of yeast: follow the manufacturer's instructions.

2 Pour the liquid into the bowl. Then add the flour (with fresh yeast if used), salt and lard.
3 Knead at minimum speed for 45 - 60 seconds. Then increase to speed 1, adding more flour if necessary, until a dough has formed.
4 Knead for 3 - 4 more minutes at speed 1 until the dough is smooth, elastic and leaves the sides of the bowl clean.
5 Put the dough into a greased polythene bag or a bowl covered with a tea towel. Then leave somewhere warm until doubled in size.
6 Re-knead for 2 minutes at speed 1.
7 Half fill four 450g (1lb) greased tins with the dough, or shape it into rolls. Then cover with a tea towel and leave somewhere warm until doubled in size.
8 Bake at 230^ / 450^ / Gas Mark 8 for 30 - 35 minutes for loaves or 10 - 15 minutes for rolls.
- When ready, the bread should sound hollow when tapped on the base.

ingredients

This quantity is for models KM600, 800 and 810. For models KM300, 400 and 410, halve the quantities and add all the flour in one go

white bread soft continental-type dough

2.6kg (5lb 12oz) ordinary plain flour
1.3 litre (21/4pts) milk
- 300g (10oz) sugar
- 450g (1lb) margarine
- 100g (4oz) fresh yeast or 50g (2oz) dried yeast

• 6 eggs, beaten
• 5 pinches salt

method 1 Melt the margarine in the milk and bring to 43^ (110^)

2 dried yeast (the type that needs reconstituting): add the yeast and sugar to the milk and leave to stand for about 10 minutes until frothy. fresh yeast: crumble into the flour and add the sugar.

other types of yeast: follow the manufacturer's instructions.

3 Pour the milk into the bowl. Add the beaten eggs and 2kg (4lb 6oz) flour.
4 Mix at minimum speed for 1 minute, then at speed 1 for a further minute. Scrape down.
5 Add the remaining flour and mix at minimum speed for 1 minute, then at speed 1 for 2 - 3 minutes until smooth and evenly mixed.
6 Half fill some 450g (1lb) greased tins with the dough, or shape it into rolls. Then cover with a tea towel and leave somewhere warm until doubled in size.
7 Bake at 200^ / 400^ / Gas Mark 6 for 20 - 25 minutes for loaves or 15 minutes for rolls.
8 When ready, the bread should sound hollow when tapped on the base.

• Makes about 10 loaves.

strawberry and apricot gâteau

ingredients: sponge 3 eggs

• 75g (3oz) caster sugar
• 75g (3oz) plain flour
  filling and decoration 150ml (1/4pt) double cream
• Sugar to taste
• 225g (8oz) strawberries
• 225g (8oz) apricots

method 1 Halve the apricots and remove the stones. Cook gently in very little water, adding sugar to taste, until soft.

2 Wash and halve the strawberries.
3 To make the sponge, whisk the eggs and sugar at maximum speed until very pale and thick.
4 Remove the bowl and the whisk. Fold in the flour by hand using a large metal spoon - do this carefully to keep the sponge light.
5 Put the mixture into two 18cm (7") greased and lined sandwich tins.
6 Bake at 180^ / 350^ / Gas Mark 4 for about 20 minutes until the cake springs back when lightly touched.
7 Turn out onto a wire rack.
8 Whisk the cream at maximum speed until stiff. Add sugar to taste.
9 Roughly chop the apricots and a third of the strawberries. Fold them into half the cream.
10 Spread this over one of the sponges, then put the other sponge on top.
11 Spread the remaining cream on top and decorate with the remaining strawberries.

meringues

ingredients 4 egg whites
- 250g (9oz) icing sugar, sieved

method 1 Line your baking tray with non-stick baking parchment.

2 Whisk the egg whites and sugar at maximum speed for about 10 minutes until it stands in peaks.
3 Spoon the mixture onto the baking tray (or use a piping bag with a 2.5cm (1") star nozzle).
4 Bake at 110^ / 225^ / Gas Mark 1 / 4 for about 4 - 5 hours until firm and crisp. If they start to brown, leave the oven door slightly ajar.
- Store meringues in an airtight tin.

shortcrust pastry

ingredients 450 g( 11 b) flour,sieved with the salt

• 5ml (1 tsp) salt
• 225g (8oz) fat (mix lard and margarine straight from the fridge)
• About 80ml (4tbsp) water

hint • Don't overmix

method 1 Put the flour into the bowl. Chop the fat up roughly and add to the flour.

2 Mix at speed 1 until it resembles crumbs. Stop before it looks greasy.
3 Add the water and mix at minimum speed. Stop as soon as the water is incorporated.
4 Cook at around 200^ / 400^/ Gas Mark 6, depending on the filling.

beefburgers

ingredients · 250g (9oz) prime sinewless beef

method 1 Cut into 2.5cm (1") cubes

2 If you don't have a mincer, use your liquidiser and mince small amounts at a time. Use speed 2 for 15 seconds maximum. Clean around the blades between one batch and the next.
3 Mix with seasonings such as chopped onion, mixed herbs (fresh or dried), coarse black pepper, and the juice and rind of a lemon.
4 Shape into 2 beef burgers and grill on medium to high heat until thoroughly cooked.

KM300,400,410 KM600,800,810

deeghaak - Voor gistmengsels.

KM300,400,410 KM600,800,810

pajdeg mjolfikt: 680g

tung jasdeg mjolvikt: 1,36kg

British type totalvikt: 2,18kg

latt jasdeg mjolvikt:1,3kg

continental type totalvikt: 2,7kg

kaka med torkad frukt totalvikt: 2,72kg totalvikt: 4,55kg

aggvitor 12 16

hastigheter 4

a Apning for store pølser

b Apning for sma polor

c kebbelager

kornkvern ⑤ A941

sitronpressive 6A995

blender ⑦ 1,2 I akryl A993A, 1,2 I glass A994A, 1,5 I rustfritt stal A996A

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CПл actHaДЯTOHKOpe3KN,HOMeIeTAN639083

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(4)

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2,6KrO6bIyHoi MykN
Yka3aHHbIe KOINHcTBa
1,3J MoJoka
INHrpdeIneHTOBpaccHTaHbIHa
300r caxapa
MoeJN KM600, 800 n 810. Jn
450r MaprapuHa
Mодeл e KM300, 400 n 410 BOЗьмITE
100r cbexnx dpoxkke nn 50r cyxnx dpoxkke
IIOJOBINHYOTyka3aHHbIXKOLNueCTB
- 6 pa36nTbIX RnU
I IO6aBbTe BcO Myk 3a OIN pa3.
- 5 Μηηοτοκ cοῦ

Cnocob npnrtoBneHna

1 Pactonnte Maprapin B MOIOke I IOBeIte Cmecb Do TEMpepaTybl 43°C.
2 Cyxne npoxk: (Tnnpoxkke, nIy KToPoro Heo6xoDIMO

BOcCTaHOBHeHne BnAroCoOpEpkAnHa) OoabBte DpOxKu n Caxap B MOJIOKO N OCTaBbTe Ha 10 MmHyT Do NOBHeHna PHebl.

CbeXne DpOxKn: NOKpoUInTe B MyKy u I06aBbTe caXap.

Dpyrne Tnbl dpoxxke: cJeDuTe yka3aHnM n3ROTOBtEnI.

3 BbIeTe MoNOKB E MKOCTb. Do6abBe pa36nTbe Jyca n 2Kr MyKn.
4 IepemeuBaIte Ha MNHmAbHo CKOpOCTn B TeueHne 1 MHyTbI, a 3aTeM Ha CKOpOCTn 1 B TeueHne eIe 1 MHyTbI. CoCKoBJIne.
5Добавыт сольи OCTашeeя COJIИЧECTBO MYKIN N epemeшаTe Ha MInHIMaJIbHOI CKOPOCTN B TeUeHne 1 MInHYtbl, 3aTeM Ha CkopoCTN 1 eUe 2-3 MInHYtbl DO NOJUYeHnO ODHOPoHD H CMecn.
6 3aONHnTE TECTOM JKcctraHbIe fOpMbI dIy BblneuKn Ha 450r, cMa3aHHbIe KInpOM, HAnoNoBHy nIN CcOpMyTe 6bNoUKN. 3aTeM HAKpoITe KxOHHbIM NIOJTeHcEM I OCTaBbTe B TEJIOM McTe, NOKa TcTO He yBeJIuHTcB O6beme BDbOE.
7 BbIneKaIte 6amOnbI npi TeMnepaType 200°C npn noJoxeHn '6' perynTopa dYXOBKn B teueHne 20 - 25 mHyt, a 6yIoouKu - 15 mHyt.
8 ToToBbI XJIe6 I3daET npn NocTyKINBaHmN NO HIXKe KOpOcKe 'nyCToI' 3ByK.
PeueNTbI paccuHTaHbI np6n3nteBHO Ha 10 6aTOHOB.

PEUENTBI (PPOOJIKEHNE)

TopcKny6HnKoI na6pknocamn

InHpeIeIeHTbI: BnCKBnTHoe Tecto

3a
75r caxapnay npnda
75r o6bIyHOn MykN
150MЛДBOHbIeCJIINBKN
- caxap NO Bkycy
225Kny6HnKn
225ra6pnikocob

Cnoco6 npriroTOBneHn

1 Pa3peKbTe a6pNkOcbl Ha nIIOBnHKn ydaIaIte KcOToKn. BapIte Ha cIa6bOM orHe C He6oJIbUIM KOINueCTBOM BOJb I Do IOCTnKeHnMgKoCTn, D06abVb N O BKycu caxap.
2 BbIMoIte n pa3peXkTe Ha noJOBuHKn IroDbl KJIy6HnKn.
3Для пи��OTOBHeNЯ TECTa B36eTeЯца n caxap Ha MaKcImaJIbHOn CKOpOCTn Do NOJyUeHnI rYcTOn CBETIOI CMEci.
4 CHMnTe Yauy N BeHnK. DoabbTe MyKy N TuaTeNbHO nepMeaIte BpyHyO C NOMoBbO 60bnWo MTeaTnNueCKo JIoKKn. BybTe OCTopoXhbl - H3bItOK MyKn CdeJaet Onapy CInuKOM rYcToi.
5Помecntte CMEcB BДBE CMa3aHbIe XINPOMФOPMbIДЯВblneKINДиamEtpm18cm.
6 BbinekaIte npn 180°C npn noJoxeHnn '4' perJyIaTopa dYxOBKn B TeueHne 20 MmhyT, noka nipor He cTaHET ynpyHm npn HaxaTN.
7 BbINOxNte Nipor Ha MeTaJIINueckyU peWSeKy.
8 B36eIte cInBn Ha MaKcImaJIbHOn CKOpOCTn Do nOnyuHeNra ryCTOn neHbI. IObaBbTe caxap no BKcy.
9 HapeKbTe a6pIKocbI KpyINbIM KycoQkAMn N doBaBte 1/3 acTb Kny6HKn. DoabBte fpykTb I NOIOBHe pnproTOBneHHoro KpeMa.
10PacnpedeIe TcmeBbHa nepBOM KOpKe PnIpora, 3aTeM PNOJXITe CBepxv BToPoI KOpK.
11PacnpedeIe octabuHcKpem Ha nobepxHocTn pnpora u ykpacbTe ero octabuec Kny6HkoN.

Mepenrn

HnrpeJeHnTbI

4aunhybIX6eIka
250r caxapno nydpbl, npocetb
1 BbIcTeJInte npOTnBeH nIuSeBbIM HeNpNIInaHOUm nepraMeHTOM.
2 B36eTe 6eKn n caxap Ha MaKcImaJIbHOJ CKOpOCTn B TeUeHne 10 MHNyT Do NOnyuEHHN CToIKOJI NeHbl.
3 BbINOKeTe IIOKoI cMeCb Ha npOTuBeHb (INI INCnOJIb3yIte KUInHapHbIM MeUOHeK CO 3BE3DOO6pa3HbIM HOCIKOM 2,5cm).
4 BbIeKaIte npn Tempepaty 110°C npn noLoXeHnn '1/4' peryIaTopa duXOBKn B TeueHne 4 - 5 YacOB Do 3aTBepeDeBaHn I NIOBJIeHn XpyCTa. EcIn y MepEHr NaHHeT npoRbIaTbc KOpuHHeBbl OTOHeK, OCTaBbTe DBepu dyXOBKn CnEka npnoTkpbItOn.
XpaHnTe MepeHnB repMeTuHoTape.

IeocuHoe Tecto

InHrpdeJeHNTbI

450r Mykn, npocerB BmecTe C cOJIbIO
- 5Mn (1ч.и.) coNN
225rJnpa (cmecb cBnHoro Jnupa n MaprapnHa, oxJaXeHHa)
- OKOJO 80Mn BOДы
He nepemewinbaite Tecto n3JINsHe dOJIrO.
1Помecntte Myky Bemkoctb.HapeKbTe Knp KpynHbIMN Ky6nKaMn IdoabBeTcMyKe.
2 3aMeuBaIte Ha ckOpocTn 1 Do Tex nop, Ioka TeCTo He cTaHETyCTbIM. OctaHOBITE 3aMeuBaHne Do TORO, KaK TECTO npNo6peTET «CaJIbHbI» BIVd.
3Добавы Te Bovyиперемшай Te Ha MInHMaJIbHOI cKOpOCTN. OctaHOBInTeперемшИВaHne,Кak TOnbKO BODa bYdET nOrnIOSeHa TECTOM.
4 BbInekaiTe npn Tempepatye 200^ npn noIooKeHnn 6' perynTopa dYxOBKn. BpemBbIneUKN 3aBNCNT O nauHKn.

InHrpdeJeHNTbI

Cnoco npurotoBneHna

BnΦ6yprepbI

250r roBanybI bIcSei KaTeOpn C ydaJIeHHbIM cyxoxNJIyMa1 1 HapeKbTe roBanyHa KycOHNpa3Mepom 2,5cm.
2 Ecnn y BAC HET MRCOPY6KN, NcNtB3yIte ROMOREHn3aTOp n rTOOBbTe 4apu He6oJIbShIMN nopCnAMy. Ppi npriROToBnEHn Fap7a NcNtB3yIte CkOpcTb 2 B TeueHnN He 60one 15 cekyHd. B npomexkyTKax MeJdy 3aRpy3kAMM Mca OChuaite HOKn.
3 CmeaTe fapUc npnpabamn, HapnPmep, c py6JIeHbIM lyKOM, CmecbIy TpaB (CBexnx INI Cyxnx), MOJToBIM YepHbIM nepcem rpy6oR oMOJa, a TAKKe C COKOM IN TePTOn CEdpoJ JIMOHa.
4 Pa3deneIte fapu nnolam m cndeaIte 2 6n6byprepa, noJkaPte nx Do nONHO rTOBHOCTn Ha rpuIe Ha cpeHem IIN BbICOKOM yPOBHe HArpeBa Do nONHO rTOBHOCTn.

157 = 20712 157.2,157.3,157.4,157.5,157.6,157.7,157.8,157.9,157.10,157.11,157.12,157.13,157.14,157.15,157.16,157.17,157.18,157.19,157.20,157.21,157.22,157.23,157.24,157.25,157.26,157.27,157.28,157.29,157.30,157.31,157.32,157.33,157.34,157.35,157.36,157.37,157.38,157.39,157.40,157.41,157.42,157.43,157.44,157.45,157.46,157.47,157.48,157.49,157.50,157.51,
01
157 1813 110

1 1
( 1,2) . ( 3,4) . ( 5,6) . ( 7,8)
1 1

IMO2019 a( 15,15,5,5,5)

[1 + \cdots + \frac{100}{2} + \frac{100}{2} + \cdots + \frac{100}{2}]

15 15 100 100 100 100
0 1K 3 111111111111111111
1,·s ,1 1,·s ,k
2| r1 - r2| ,r1,r2 z,1
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
1. | x - 2| = | x + 3| - | 2 - x| .

同日・の旧》

5 1

11000000 11000000 11000000 11000000 11000000 11000000

1

IMO2019 x^3y^3( mod p)

111 1

111 1
r0211mm？ 11
15.16.13 15.13.11 14.14.10 14.14.12 14.14.11 14.14.10 14.14.10
110-2 115
S木弟形 COBD = S COD + S BDO = S BOC +

111

1

2 1

1

S木弟形 COBD = S COD + S_ BDO

( 2) Sn = na1 + ( n - 1) 2

10^211^212^2 ② 11 × 12 = 217

S木弟形 COBD = S COD + S BDO = S COD + S_ BDO

S APQ = S AQP - S_ AQP = 12

11111111

m : x = 1 或 3x + 4y + 1 = 0

11 : ( 2 - 1) = 0 · 3^201 - 1 · 1^301

10^3 < | | < 10^6 时.

它恰好 x,y 且 x^2 + y^2 - 4x + 3 = 0 有无穷多的解.

11 S ACD = S COD + S BDO - S CDA

它恰好 x,y 且 x^2 - y^2 = 1 时,方程有两个不相等的实数根

a1 = 23,an + 1 = an - an - 1

10^ 15^ 10^ 15^ 10^ 15^ 15^ 15^ 15^ 15^ 15^ 15^ 15^ 15^ 15^ 15^ 15.

111 111 111 111 111 111 111 111 111

15 < 10 < 17

1054 1054

• 12000000000000000000000000000000

-

1. 10 < 20 < 30 即 1 < 20 < 2 或 1 < 20 < 2 即 k < 1

K

S木弟形 COBD = S COD + S_ BDO

2 2

11 1111000000000000000000000000000

m = 311

1111111111111111111111

8 1107 1107 1107 1107 1107 1107 1107 1107

111 1

1 1

Aeonr 15x99

1 1

( \left{ {1,2,3}\right} \Rightarrow \left{ {1,3,4}\right} \Rightarrow \left{ {2,3,4}\right} \Rightarrow \left{ {3,4}\right} \Rightarrow \left{ {4,5}\right} \Rightarrow \left{ {5,6}\right} \Rightarrow \left{ {6,7}\right} \Rightarrow \left{ {7,8}\right} \Rightarrow \left{ {8,9}\right} \Rightarrow \left{ {9,10}\right} \Rightarrow \left{ {10,11}\right} \Rightarrow \left{ {11,12}\right} \Rightarrow \left{ {12,13}\right} \Rightarrow \left{ {13,14}\right} \Rightarrow \left{ {14,15}\right} \Rightarrow \left{ {15,16}\right} \Rightarrow \left{ {16,17}\right} \Rightarrow \left{ {17,18}\right} \Rightarrow \left{ {18,19}\right} \Rightarrow \left{ {19,20}\right} \Rightarrow \left{ {20,21}\right} \Rightarrow \left{ {21,22}\right} \Rightarrow \left{ {22,23}\right} \Rightarrow \left{ {23,24}\right} \Rightarrow \left{ {24,25}\right} \Rightarrow \left{ {25,26}\right} \Rightarrow \left{ {26,27}\right} \Rightarrow \left{ {27,28}\right} \Rightarrow \left{ {28,29}\right} \Rightarrow \left{ {29,30}\right} \Rightarrow \left{ {30,31}\right} \Rightarrow \left{ {31,32}\right} \Rightarrow \left{ {32,33}\right} \Rightarrow \left{ {33,34}\right} \Rightarrow \left{ {34,35}\right} \Rightarrow \left{ {35,36}\right} \Rightarrow \left{ {36,37}\right} \Rightarrow \left{ {37,38}\right} \Rightarrow \left{ {38,39}\right} \Rightarrow \left{ {39,40}\right} \Rightarrow \left{ {40,41}\right} \Rightarrow \left{ {41,42}\right} \Rightarrow \left{ {42,43}\right} \Rightarrow \left{ {43,44}\right} \Rightarrow \left{ {44,45}\right} \Rightarrow \left{ {45,46}\right} \Rightarrow \left{ {46,47}\right} \Rightarrow \left{ {47,48}\right} \Rightarrow \left{ {48,49}\right} \Rightarrow \left{ {49,50}\right} \Rightarrow \left{ {50,51}\right} \Rightarrow \left{ {51,52}\right} \Rightarrow \left{ {52,53}\right} \Rightarrow \left{ {53,54}\right} \Rightarrow \left{ {54,55}\right} \Rightarrow \left{ {55,56}\right} \Rightarrow \left{ {56,57}\right} \Rightarrow \left{ {57,58}\right} \Rightarrow \left{ {58,59}\right} \Rightarrow \left{ {59,60}\right} \Rightarrow \left{ {60,61}\right} \Rightarrow \left{ {61,62}\right} \Rightarrow }

a1 = 23,a2 = 49,b1 = 58,b2 = 79

11111111111111111111111111111

a1 = 12a0 + 32b_0^2

111

37 (106) 15.19g(10.2) 6400 ？ Imogen

133