A number is 12 / 5. What's 8 / 3 of it

A number is 12 / 5. What's 8 / 3 of it

12/5*8/3=32/5

Write the formula with 2.4.6.8.10.12.14.16? () + () = () + ()=（
Write the formula with 2.4.6.8.10.12.14.16? () + () = () + () = () + () = () + () - () = () - () - () = () - () = () - ()

That's about it~
2+16=4+14=6+12=8+10
10-2=12-4=14-6=16-8

If two of the equations x ^ 2 - MX + 1 = 0 are α, β, and α > 0,1 < β < 2, then the value range of the real number M

The equation is a quadratic equation with two roots, then △≥ 0, i.e. m ^ 2-4 ≥ 0, m ≥ 2 or m ≤ - 2 α＞ 0 should be divided into five cases. Discuss 0 ＜ α＜ 1 α = 1 1 ＜ α＜ 2 α = 2 α＞ 2, Let f (x) = x ^ 2-mx + 1. When 0 ＜ α＜ 1, solve the inequality group F (1) ＜ 0; f (0) ＞ 0; f (2) ＞ 0, and get 1 ＜ m ＜ 5 / 2, because m ＜ 2

Given that a and 2b are reciprocal to each other, - C and D / 2 are opposite to each other, | x | = 4, find 4ab-2c + D + X / 4
It will be handed in to the teacher tomorrow morning!

4ab-2c+d+x/4
=2*2ab+(-2c+d)±4/4
=2+0±1
=3 or 1

The domain of function f (x) = LG [4 ^ (x + 1) - 9 * 2 ^ x + 2]
Excuse me, I have two answers to this question: x1, do you need to omit one of them?

No, you need both. It seems that you will know the process

If (x ^ m ÷ x ^ 2n) &# - 179; △ x ^ M-N and &# - 188; X & # - 178; are similar terms and 2m + 5 = 6, find the value of M, n

(x^m÷x^2n)³÷x^m-n
=X^(m-2n)/x^(m-n)
=X^(m-2n-m+n)
=x^(-n)
It is the same kind of term as & # 188; X & # 178
Then - n = 2
n=-2
2m+5=6
m=1/2

Finding the inverse function of y = LG (4 / x + 2 - 1)

y=lg [4/(x+2) -1]
10^y = 4/(x+2) -1
4/(x+2) =10^y + 1
x + 2 = 4/(10^y + 1)
x = 4/(10^y + 1) -2
So the inverse function is:
y = 4/(10^x + 1) -2
But your original style is not very clear. Do you think it's this?

If the function f (x) = 13x3-x has the minimum value on (a, 10-a2), then the value range of a is___ ．

It is known that if f ′ (x) = x2-1 and x2-1 ≥ 0, then x ≥ 1 or X ≤ - 1 can be obtained. Therefore, when x ∈ [1, + ∞), (- ∞, - 1], f (x) is an increasing function, and when x ∈ [- 1, 1], f (x) is a decreasing function. Because f (x) = 13x3-x has a minimum value on (a, 10-a2), the open interval (a, 10-a2) must contain x = 1, so the minimum value of F (x) is the minimum value of F (1) = - 23, From F (x) = - 23, we can get 13x3-x = - 23, then we can get (x-1) 2 (x + 2) = 0, that is, we have f (- 2) = - 23, so the following inequality holds: - 2 ≤ a < 110-a2 > 1, we can get - 2 ≤ a < 1, the answer is: [- 2, 1]

Given the function f (x) = x2 + 2x + A, f (BX) = 9x2-6x + 2, where x ∈ R, a and B are constants, the solution set of the equation f (AX + b) = 0 is obtained

From the meaning of the title, we know that f (BX) = b2x2 + 2bx + a = 9x2-6x + 2, a = 2, B = - 3, f (2x-3) = 4x2-8x + 5 = 0, ∵ △ 0, and the solution set of the equation f (AX + b) = 0

AB is a real symmetric matrix, and ab = ba. If a has n distinct eigenvalues, it is proved that there exists an orthogonal matrix P, so that p'ap and p'bp are diagonal matrices

Suppose that what you said "ab is a real symmetric matrix" is actually "a and B are real symmetric matrices"
Take the orthogonal matrix P so that p'ap = D is a diagonal matrix
Let C = p'bp, DC = CD from the condition, write out every element, and then use the diagonal elements of D to be different, that is, C is a diagonal matrix
In fact, even if the condition of "a has n distinct eigenvalues" is removed, the conclusion is still valid, but the proof needs one more step