Math Puzzle Teach everyone 20

Solution: Equation There are two unequal real number roots δ 2(m 1)]2 4(m2 2m 3) 16m 16 0 solve m 1 and equation has a root of 0 m2 2m 3 0, i.e. (m 3) (m 1) 0 solution gives m1 1m2 3 and m 1 m1 1 should be rounded off m 3 When m 3, the equation is deformed to x2 (k 3) x k 4 0 x1 and x2 are equations.

The two real roots of x1 x2 k 3 and x1x2 k 4 if|x1－x2|1, then there is (x1 x2)2 4x1x2 1 (k 3)2 4( k 4) 1 i.e. k2 2k 8 0,(k 4)(k 2) 0 k1 2,k2 4 when k 2 δ [k 3)]2 4( k 4) k2 2k 7 ( 2)2 2 ( 2) 7 1 0 When k 4, δ k2 2k 7 42 2 4 7 1 0 k 2 or 4 There is a real number k 2 or 4, such that the absolute value of the difference between the two real roots of the equation is 1.

Analysis: This problem is an exploration of existential problems, using discriminant formulas and the relationship between roots and coefficients, and direct reasoning according to the meaning of the question is the basic method to solve this kind of problem.

One of the two unequal real roots of x2-2(m+1)x+m2-2m-3=0 has a root of 0

Then x=0 satisfies the equation, then there is m2-2m-3=0

So m=3 or m=-1

Substituting x2-(k-m)x-k-m2+5m-2=0

At this time, there is: x2-(k-3)x-k-9+15-2=0

or x2-(k+1)x-k-1-5-2=0

That is: x2-(k-3)x-k+4=0

or x2-(k+1)x-k-8=0

To make the difference between the two real roots x1 of the equation x2-(k-m)x-k-m2+5m-2=0 about x, the absolute value of the difference between x2 is 1

i.e. (x1 - x2)2 = 1

At the same time: x1+x2 = (k-m).

x1*x2 = -k-m2+5m-2

At this point, we get 2 systems of equations:

m = 3x1+x2 = k-3

x1*x2 = -k+4

x1 - x2)2 = 1

m = -1

x1+x2 = k+1

x1*x2 = -k-8

x1 - x2)2 = 1

Since (x1 - x2)2 = (x1 + x2)2 - 4x1x2 = 1

This results in: x1 - x2)2 = (x1 + x2)2 - 4x1x2 = 1 = (k-3)2 - 4(-k+4).

or (x1 - x2)2 = (x1 + x2)2 - 4x1x2 = 1 = (k+1)2 - 4(-k-8).

Do the rest yourself.

2(m-1))^2-4m^2+8m+12

4m^2-8m+4-4m^2+8m+12

So there are always two unequal roots.

When x=0m2-2m-3=0

m1=3 m2=-1

x2-(k-m)x-k-m2+5m-2=0x1-x2=((x1+x2) 2-4x1x2) (1 2)((k-m) 2+4k+4m 2-20m+8) (1 2)=1k 2-2mk+m 2+4k+4m 2-20m+8=1k 2+(4-2m)k+5m 2-20m+7=0, i.e. k 2-2k-8=0

or k 2 + 6 m + 32 = 0 (no solution).

k1=5 k2=-3

[(1+1)*2+1]*2=10 Sell 9 eggs.

The second person buys half of the eggs and one egg and leaves one egg, so if you don't buy the one egg, you get two eggs, and the two eggs are half of the eggs that the first person has left, so the second person buys four eggs, and the same goes for the first person who buys 10 before they buy it.

The second person buys half and one of the remaining eggs, and there is still one egg left in the basket at this time, indicating that half of the eggs in the basket at this time are two, that is, there are 4 left after the first person buys it, and the first person buys half of the eggs in the basket and one again, indicating that half of the eggs in the basket at this time are 5, that is, there were 10 eggs at the beginning.

2. Solution: If 84 disinfectant water is x bottle, then hand sanitizer is (56-x) bottle according to the topic: 3x+5*(56-x)=216

Solution: x=32 (bottle).

That is: 84 disinfectant a total of 32 bottles, hand sanitizer 56-32 = 24 bottles If "84" is calculated according to 5 yuan bottle, and the washed liquid is calculated according to 3 yuan bottle, then the pharmacy collects as follows:

5 * 32 + 3 * 24 = 232 (yuan).

If the school paid a total of $232, then the pharmacy was overpaid by $16, and the school lost $16. When the school goes to the pharmacy for settlement, the pharmacy should supplement the school with 16 yuan.

If the school paid a total of 216 yuan, no one would have lost. When the school settles at the pharmacy, the pharmacy should reissue the invoice according to the correct commodity **, with a total amount of 216 yuan.

1.Let B transport x boxes each time, then A can get the equation 8x=5(x+4)+13 each time x+4 boxes, and x=112There seems to be a problem with the title.

When the accountant reconciled, it was found that the pharmacy calculated the "84" disinfectant at 3 yuan per bottle".

Among them, "84" disinfectant is 3 yuan per bottle".

It's all said that it's 3 yuan, how can it be wrong? That's right to calculate it at 3 yuanAfter removing the parentheses, 408 75+x*12=208 can be solved to get x, and then substitute x into the original formula to calculate the result.

x-(x+4)*5=13 x=112, the question is wrong, and the 84 disinfectant is originally 3 yuan.

75+x*12=208 x=422/25(408/75+422/25）*12=6696/25=