It is known that the coefficient of quadratic term of quadratic function f (x) is a, and the two roots of equation f (x) - x = 0 are X1 = 1, X2 = 2 (1) if equation f (x) - x ^ 2 = 0 has two phases If a < 0, the maximum value of F (x) is g (a), and the range of a * g (a) is obtained

It is known that the coefficient of quadratic term of quadratic function f (x) is a, and the two roots of equation f (x) - x = 0 are X1 = 1, X2 = 2 (1) if equation f (x) - x ^ 2 = 0 has two phases If a < 0, the maximum value of F (x) is g (a), and the range of a * g (a) is obtained

Let K (x) = f (x) - x, then K (x) = a (x-1) (X-2) = a (x ^ 2-3x + 2)
1.f(x)-x^2=a(x^2-3x+2)+x-x^2=(a-1)x^2+(1-3a)x+2a
If △ = (1-3a) ^ 2-8a (A-1) = 0, a = - 1
So, f (x) = - 2x ^ 2 + 4x-2
2.f(x)=a(x^2-3x+2)+x=ax^2+(1-3a)x+2a
g(a)=(-a^2+6a-1)/(4a)
a*g(a)=(-a^2+6a-1)/4
According to the knowledge of quadratic function, a * g (a) belongs to (negative infinity, - 1 / 4)

If the quadratic function y = f (x) satisfies f (0) = f (2), X1 and X2 are the two real roots of the equation f (x) = 0, then X1 + x2 +?

Because f (x) is a quadratic function and f (0) = f (2)
Then the axis of symmetry is x = 1
According to Weida's theorem
x1+ x2=-b/a
The equation of axis of symmetry is - B / 2A = 1
Then - B / a = 2
x1+x2=2

Simple calculation of 21.7-5 / 8 + 8.3-3 / 8

21.7-5/8+8.3-3/8=21.7+8.3-5/8-3/8=(21.7+8.3)-(5/8+3/8)=30-1=29

In trapezoidal ABCD, ad is parallel to BC, and the median EF intersects diagonal AC and BD at M and N. if EF = 18 and Mn = 8, BC =?

The most annoying part of this problem is that I don't know who is big and who is small in AD and BC, so I have to discuss it in different situations
Suppose ADB
EM=BC/2,NF=BC/2
EM+NF=BC
EM+NF=EF-MN=10
BC=10

Fill in the brackets of equation 6 / 1 = () / 1 + () / 1 with different natural numbers to make the equation hold

1/6=1/9+1/18=1/8+1/24=1/10+1/15

Is the trace of a positive semidefinite Hermite matrix equal to the sum of its eigenvalues? What are the characteristics of its eigenvalues?

It is equal to, because the trace of any square matrix is the sum of its eigenvalues
All eigenvalues of Semidefinite Hermite matrices are real numbers and are greater than or equal to 0

A sum of two digit, ten digit and one digit
[continued] is 11. If the number is x, then the ten digit number is -. This two digit number can be expressed as - --- (without simplifying the result)

The sum of a two digit, ten digit and a digit is 11. If a digit is x, then ten digit is [11-x]. This two digit can be expressed as [x + 10 (11-x)] (without simplifying the result)
This is my conclusion after meditation,
If not, please ask, I will try my best to help you solve it~
If you are not satisfied, please understand~

If the determinants of two matrices are equal, the two matrices are equal

No
If the matrix is equal, the determinant is equal
Otherwise, it does not hold
as
1 1
0 1
And
1 0
0 1
Determinants are equal, matrices are not equal

In the formula x = a + B / AB (AX-1 is not equal to 0), given a, x, then B=

Because AB is in the denominator position, AB is not zero. You can multiply AB on both sides to get: ABX = a + B, and move B to the left to get B (AX-1) = a
And because AX-1 is not equal to 0, B = A / (AX-1)

Programming for "narcissus number". The so-called narcissus number refers to a three digit number, the number of its cube and equal to the number itself

Algorithm: can enumerate all three digits, and then decompose each digit to judge
C language (three digit enumeration method)
#include
main()
{
int i,s1,s2,s3;
for(i=100;i