Olympiad math problems, to answer, to answer, to hurry,

1. Solution: (1-1 2 2) (1-1 3 2)....(1-1/1999^2)(1-1/2000^2)

2、x^2+y^2+5/4=2x+y

x^2-2x+y^2-y+5/4=0

x^2-2x+1+y^2-y+1/4=0

x-1)^2+(y-1/2)^2=0

x=1,y=1/2

xy/(x+y)=1/3

3、x^2+x-1=0

x^2+x=1

x^3+2x^2+3

x^3+x^2+x^2+3

x(x^2+x)+x^2+3

x+x^2+3

5. The solution set of (2a-b)x+a-5b 0 is x 10 72a-b)<0, [-a-5b)] (2a-b)=10 73a=5b, (2a-b)<0

The solution of ax b is xx<3 5

The solution set for ax b is .

There are as many as you want. The main thing is to pick something that suits your degree.

1.Calculation: (1-1 2 2) (1-1 3 2)....(1-1/1999^2)(1-1/2000^2)

2.Knowing that x,y satisfies x 2+y 2+5 4=2x+y, find the value of the algebraic formula xy (x+y).

3.If x 2 + x - 1 = 0, calculate: x 3 + 2 x 2 + 3

4.Put (x 2+x-1) 6 to get (a12) x 12+(a11) x 11+....(a2) x 2+(a1)x+a0, then the value of a12+a10+a8+a6+a4+a2+a0 is (a12, a11, etc. represent a number).

5.The solution set of the inequality about x (2a-b) x+a-5b 0 is known to be x 10 7, then the inequality about x.

The solution set for ax b is .

Solution: (1) Original formula = 2001 4000

2) Original = 1 3

3) Original = 4

5）x＜3/5

Question 1: 56 square decimeters.

Solution: Suppose the strip of 1 decimeter is cut off for one portion, so.

The first side is cut off by 2 decimeters, and the adjacent second side is cut off by 1 decimeter, making a total of three parts.

Since the overlapping part is 2x1 = 2 square decimeters, the area of the triplet is 25 + 2 = 27 square decimeters.

So each serving is 9 square decimeters.

That is, the side length of the original square plank is 9 decimeters.

The remaining area is (9-1) x (9-2) = 56 square decimeters, and the second question is 40.

Solution: Suppose they eat 8 apples and 4 pears a day, and the pears can be eaten just after a few days.

But in fact, they eat 5 apples and 4 pears a day. In this way, there are 3 more apples per day, but there are actually 15 apples left after a few days, which means that 15 3 = 5 days have been eaten, so when the mother buys the apples, 5x5 + 15 = 40.

1) Let the side length of the cube be a, then a 2 - a-2)*(a-1)=25a 2 -a 2 +3a-2=25

3a=27a=9 The remaining area A 2 -25=9 2 -25=56 square centimeters 2) Put 8 apples (4*2=8) and 4 pears in a pile, a total of several piles, eat 5 apples and 4 pears from the first pile on the first day, and 8-5=3 apples left, and eat 5 apples and 4 pears in the second pile on the second day, leaving 8-5=3 apples.

There are 3 apples left in each pile, for a total of 15.

i.e. a total of 15 3=5 heaps.

Mom bought apples 5*8=40 pcs.

(1) Because the question says to cut off 1 decimeter on the second side of the adjacency. So there is a small overlapping part that is only counted once, and the area of this part is: 1 2 = 2 square decimeters.

Because it was cut twice and only counted once, 25 should be added to 2, which equals 27. And because the stone is square and the planks are square, the two pieces are equal in length. The two pieces are stacked together to form a rectangle with a width of 3 and a length that is the side length of the original square.

Then the side length of the square is 27 3 = 9 decimeters. It turns out that the area of the square is 9 9 = 81 square decimeters. Subtract 25 and you're left with 56 square decimeters.

2) Because apples only count twice as many as pears, and pears are eaten 4 a day. If you want to maintain a 2x relationship, then you need to eat 2 4 = 8 apples a day, but only 5 are eaten in the question, which is 3 less. In the end, 15 more apples are 3 a day.

then a total of 15 3 = 5 days. Eating 5 apples a day for these 5 days, a total of 5 5 = 25 apples, plus the remaining 15 is a total of 40 apples.

Do you want steps? Question 1 Because it is a four-digit number and the sum is 2000, the thousand digits can only be 1 Let the number be 1abc

then 1000+100a+10b+c+1+a+b+c=2000

Simplification to 101a+11b+2c=999

Assuming a=8, then it is 808+11b+2c=999, no matter what value b and c take, 808+11b+2c is less than 999, so a>8, so a can only take 9, then 101a+11b+2c=101*9+11b+2c=909+11b+2c=999

11b+2c=90 Suppose b takes 9, then 11*b=99>90 rounded off b takes 8, then 88+2c=90 c=1

b takes 7, then 77 + 2c = 90 c = obviously wrong b = 6 66 + 2c = 90 c = 12 is greater than 10 c is greater than 10 so it is not right so a = 9 b = 8 c = 1 this number is 1981

Question 2(4-2) (1 3000 - 1 4000) = 24000

Question 3 Let the elder brother be x 3 years ago, and the younger sister be y

x=3yx+5)=2(y+5) The solution gives x=15 y=5

So my sister is 5+2=7 years old this year.

Question 4 Let the cost of A be x and B be y

x+y=220

x*(1+30%)+y*(1+20%)]90%=220+23

The solution is x=60 y=160

There are 26 books on the upper floor and 22 copies on the lower floor.

Let the upper layer x1 and the lower layer x2 according to the prompts: (x1-10) x 2 = x2 + 10 and (x2 - 10) x 3 = x1 + 10 to solve the equation.

Question 2: 21 people 47-11-30=6 There are 6 people who get 5 points in two subjects 30 divided by 2 plus 6 to get 21 is the number of languages.

Question 3: 9 grams Let x be the number of grams of the original wine, and the amount of alcohol before and after does not become the equation: x x 45% = (x + 16) x 25%.

Question 4: 2500 grams Let x be 45% grams of sugar water to get the equation: x x 45% + 4000 - x) x 5% = 4000 x 30%.

Question 5: Cup 24%.

26 22

21 set the original liquor x grams.

x*45%=（x+16）*25%

x*20%=16*25%

x = 20 grams.

20*45%=9 grams.

There are 9 grams of edible alcohol in the wine.

4000 * ((45%-30%) (45%-5%)) = 1200 grams of wine with x glasses of wine at a concentration of c

x*c/（x+1）=25%

x*c+1）/（x+1）=40%

x=17/3

c=5/17

17 3 * 5 17 = 5 3 cups.

The original 5 3 cups of alcohol with a concentration of 5 17

Question 1: There are several books on the upper and lower shelves. If you take ten copies from the upper layer and put them on the lower layer, the number of copies in the lower layer is twice as large as the number in the upper layer; If you take ten copies from the lower layer and put them on the upper layer, the number of copies in the upper layer is 3 times that of the lower layer.

The original books ( ) on the upper floor, and the original books ( ) on the lower floor.

Equation: There are x books on the upper shelf and y on the lower shelf.

Equation: x-10=2(y+10).

3（x+10)=y-10

There is no point in such a hurry, and the system of columns and equations has come out.

Velocity = 16m s when you go

So every 400 16 = 25 seconds at a traffic light.

Because every time it turns green on arrival.

So each traffic light is 25 seconds apart in the direction it is going

Green 1 time t (turn green).

Green 2 at t+25

Since the traffic light period is 30+5+30 = 65s, it is equivalent.

Green 1 time t (turn green).

Green 2 Moment T-40 (turn green).

So on the way back, the opposite direction becomes.

Green 1 time t (turn green).

Green 2 Moment T-40 (turn green).

So 400 meters to drive 40s.

That's 10 m s, that's 36 kilometers per hour.

If you can solve the problem with equations, it will be solved like this:

Let a pool of water be a

then t=a (a 1-a.)

If you can't use equations, you can understand this problem like this:

A can slow down the water in two pools by opening it alone for three hours, and B can just finish the water in three pools after three hours, so that after three hours, the two pools of water that A has filled and the original pool of water are just three pools of water, which is just enough for B to finish, so the pool is empty after three hours.

When the nail pipe is opened separately for 1 and a half, the pool can be filled.

That is, the armor tube is opened separately for 1 hour to fill 2 3 pools.

Open the B pipe separately, and the full pool water can be discharged in one hour.

At the same time, open for 1 hour and release water 1 3

So 3 hours to put it out.

This is still an Olympiad topic.

It's so easy, isn't it?

1 (1 (1 and a half)+1) = 2 5 hours.

1 and 2 hours = 90 minutes 1 hour = 60 hours and minutes 1 90 + 1 60 = 1 36 1 divided by 1/36 = 36 minutes.

1.(10*5 6+10+60) (1-2 5-2 5*5 6)=t2(100+60+35+60*3 4) (1-2 5-3 4*2 5)=800 meters.

3.(420-60-60*3 4+35) (2 5+3 4*2 5)=500m.

Decimeter = 20 cm, 1 decimeter = 10 cm.

8*5*2 (20*10) = cm.

1.Ton.

2.800 meters.

3.220 meters.

4.(When the water is completely submerged in the iron) the water rises by centimeters.

You can't do it without x.

Suppose the first three people use the last day to get A's turn, suppose B does x every day, and C does y every day, then x+1 2y=1 15 then y+1 3 1 15=1 15 y=2 45 x=2 45 But their work efficiency is different, so assuming failure, the first last day is B's turn Suppose B does x every day and C does y every day, then x+y+1 30 =x+1 30 finds y=1 30, y+1 15+1 3x=x+1 15 finds x=1 20 Team B will need to repair 20 days alone, and Team C will need to repair 30 days alone.

1. On the first day of school, every two students meet each other to shake hands and greet each other, and the whole class of 40 people shakes hands.

Times? Times? 2. The second term of an equal difference series is 2 8, and the third term is 3 1, find the 15th term of this equal difference series.

Item 15 is .

3. There are 36 students in the second class of the fifth grade, and the class leader Wu Hong went to buy a picture book for everyone, one for each person. When I came back, I forgot to count the money, but I only remembered that it was 1 1 yuan. Q: Each picture book is worth RMB.

4. The oil in the east oil inventory is 6 times that of the oil in the west oil, if the two oil depots each increase 30 tons of oil, the oil in the east oil will be 3 times the oil in the west oil stockpile, how many tons of oil in the two oil depots?

The east oil depot used to store tons of oil, and the west oil depot used to store tons of oil.

5. A six-digit abcdek, multiplied by e, the original number is kabcde, what is the original number? (Different letters represent different numbers) The original number is .

6. 500 people from Qingquan Primary School participated in the entrance ceremony of the sports meeting, a line of 20 people, the distance between the two lines was 3 meters, and the rostrum was 18 meters, and they passed the rostrum at a speed of 30 meters per minute, which took minutes.

7. In the figure below, there are a total of rectangles.

7 can be turned into a circular decimal, ask what is the number in the 1995th place after the decimal point of this circular decimal? This number is .

9. The three sides of a triangle are three consecutive two-digit even numbers, and the sum of their mantissa numbers is divisible by 7 to find the maximum perimeter of this triangle.

The circumference is . 10. There is a fraction, if the numerator and denominator are added to 1, the fraction becomes 1 2, if the numerator and denominator are subtracted by 1, the fraction becomes 2 5, find this fraction.

This score .

11. One day, a jewelry store in a certain city was stolen from diamonds worth tens of thousands of yuan. After reporting the case, after three months of investigation, it was ascertained that the perpetrator must be one of A, B, C, and D. After interrogation, the confessions of the four men were as follows:

A: On the day the diamond was stolen, I was in another city, so I'm not a criminal.

B: D is a criminal.

C: B is a thief, and three days ago, I saw him selling a diamond on the black market.

D: B has an enmity with me and intends to frame me.

Because of the inconsistencies in the confessions, it is impossible to determine who is the culprit.

After the panic test, it is known that only one of the four people is telling the truth, so who is the criminal?

The offender is . 12. There are 253 students in the fifth grade of Qingfeng Primary School, and the school has organized a math group, a recitation group, and a dance group, and stipulates that each person participates in at least one group and at most two groups, so how many people participate in the same group at least? Person.