F (x) = ax & sup2; + BX (a ≠ 0), if the axis of symmetry of the function is x = 1 and the equation f (x) = x has equal real roots (1) Finding the analytic expression of F (x) (2) If f (x) domain [M, n] and range [2m, 2n], find the value of real number m, n

F (x) = ax & sup2; + BX (a ≠ 0), if the axis of symmetry of the function is x = 1 and the equation f (x) = x has equal real roots (1) Finding the analytic expression of F (x) (2) If f (x) domain [M, n] and range [2m, 2n], find the value of real number m, n

The axis of symmetry is x = 1, that is - B / (2a) = 1, that is, B = - 2A
And the equation f (x) = x has equal roots, that is: ax ^ 2 + (B-1) x = 0 has equal roots, because x = 0 is one of them, so both are 0, that is, B = 1
So a = - 1 / 2
1)f(x)=-x^2/2+x
2）f(x)=-1/2(x-1)^2+1/2
If the domain contains x = 1, then the minimum value is 2m = 1 / 2, and M = 1 / 4,
The maximum value is 2n = f (n) = - n ^ 2 / 2 + N, n = 0, or - 2, which is inconsistent
Or 2n = f (m) = 15 / 32, get n = 15 / 64, not consistent
If the domain does not contain x = 1, the maximum and minimum values are obtained at the endpoint
From 2n = f (n), we can get n = 0, or - 2, so the interval [- 2,0] is consistent
From 2n = f (m), 2m = f (n), it is obtained that:
2n=-m^2/2+m
2m=-n^2/2+n
By subtracting the two formulas and dividing them by N-M: 2 = (n + m) / 2-1, we get n + M = 6, and substituting them, we have no solution
Therefore, only m = - 2 and N = 0

The minimum value of quadratic function f (x) is 1, and f (0) = f (2) = 3. If f (x) is monotone in the interval [2a, a + 1], find the value range of A

If f (0) = f (2) = 3, then the axis of symmetry is the midpoint of 0,2, that is, x = 1
If the minimum value is 1, then f (x) = a (x-1) ^ 2 + 1
Substituting f (0) = a + 1 = 3, we get a = 2
So f (x) = 2 (x-1) ^ 2 + 1
It is monotone in the interval [2a, a + 1], indicating that the axis of symmetry is not in the interval
one

Fill in the operation symbol: 8 + 8 = 1000
If we want to make the formula true, we can't use 88888 and so on, we can only use 8

[(8+8)*8-(8+8+8)/8]*8=1000

What can we deduce if the k-th power of n-order matrix A is equal to 0
If a is a matrix of order n and a ^ 3 = 0, then the inverse matrix of (e-A) =?

a^3-e=-e
(a-e)(a^2+a+e)=-e
(e-a)(a^2+a+e)=e
(e-a)^(-1)=a^2+a+e
For reference only

There are 1,2,3,4,5,6,7,9,10,11,12,13 numbers in the brackets below to make the equation hold. (each number can only be used once) () + () = () - () = () multiplied by () = () divided by () = ()

1 10 2 2 3

Let a be a third-order matrix, and | a | = half, find the value of | (3a) ^ - 1 - 2A ^ * |

(3a) ^ (- 1) = (1 / 3) a ^ (- 1) a * = | a ^ (- 1) = (1 / 2) a ^ (- 1) so | (3a) ^ - 1 - 2A ^ * | = | (1 / 3) a ^ (- 1) - (1 / 2) a ^ (- 1) | = | - 2 / 3) a ^ (- 1) | = (- 2 / 3) ^ 3 | a ^ (- 1) | = (- 2 / 3) ^ 3 * 2 = - 16 / 27

Sequence, (2), (4,6), (8,10,12), (14,16,18,20), then the sum of the nth group of numbers is____ ?
Even numbers are divided into arrays, (2), (4,6), (8,10,12), (14,16,18,20), then the sum of the nth group of numbers is____ It is represented by a formula containing n

The first number of the nth group is [(n-1 + 1) * (n-1) / 2 + 1] * 2 = n ^ 2-N + 2
The nth number is [(n + 1) * n] * 2 = n ^ 2 + n
So the sum of the nth group number is [(n ^ 2-N + 2 + n ^ 2 + n) * n] / 2
=n^3+n

It is proved by mathematical induction that 32n + 2-8n-9 (n ∈ n) can be divisible by 64

How to make the formula equal to 24?
Addition, subtraction, multiplication and division can be used in it, but each number can only be used once

1: (3 + 5 ÷ 5) × 62: (3 + (5 ÷ 5)) × 63: (3 × (5 + 5)) - 64: 3 × (5 + 5) - 65: (5 + 5) × 3 - 66: ((5 + 5) × 3) - 67: (5 ÷ 5 + 3) × 68: ((5 ÷ 5) + 3) × 69: 6 × (3 + 5 ÷ 5)10: 6 ...

The absolute value of X is equal to the root sign 3. The square + (a + B + CD) of the algebraic expression x is multiplied by a + B in the root sign of X + and the root sign CD with the root index of 3
Sorry, because the number of words is not enough, the condition is written here: real number Z, B are opposite to each other, C, D are reciprocal to each other
I'm very interested in mathematics. I have to figure it out. No, or I can't eat

The real numbers a, B are opposite to each other, C, D are reciprocal to each other, x = √ 3, request algebraic formula X & # 178; + (a + B + CD) x + √ (a + b) + (CD) ^ (1 / 3) a, B are opposite to each other, so a + B = 0; C, D are reciprocal to each other, so CD = 1, so: X & # 178; + (a + B + CD) x + √ (a + b) + (CD) ^ (1 / 3) = (± √ 3) &# 178; + (0 + 1) (±