Decomposition factor: 2m power of 3 + m power of 3 + 2-52

Decomposition factor: 2m power of 3 + m power of 3 + 2-52

=(m power of 3) & #178; + m power of 9 × 3-52
=(m power of 3 + 13) (m power of 3 - 4)

Decomposition factor 1. M + 1 power of a + 2m power of a - m power of a
1. M + 1 power of a + 2m power of a - m power of a
2. The second power of a (B-C) + 4 (C-B) - 2Ac + 2Ab

M + 1 power of a + 2m power of a - m power of a
=M power of a (a + A & sup2; - 1)
2）
The second power of a (B-C) + 4 (C-B) - 2Ac + 2Ab
=（b-c）（a²-4）+2a（b-c）
=（b-c）（a²+2a-4）

If the m power of a is half and the 2n power of B is one third, then the 2m plus 6N power of a =?

2m power of a + 6N power of B
=(m power of a) & # 178; + (2n power of B) & # 179;
=（1/2）²+（1/3）³
=1/8+1/27
=（27+8）/8*27
=35/216

Solving equation [1 / (cosx SiNx)] ^ 2-4 [cosx / (cosx SiNx)] + 2 = 0

From the original formula, we can get 1 / (cosx SiNx) ^ 2 = 4cosx / (cosx SiNx) - 2 = 2 (SiNx + cosx) / (cosx SiNx) so 1 / (cosx SiNx) = 2 (SiNx + cosx) then 2 (SiNx + cosx) (cosx SiNx) = 1 = 2 (COS ^ 2x-sinx) = 2cos (2x) so cos2x = 1 / 2 then 2x = ± π / 3 so x = ± π / 6

1: Given that the image of a first-order function passes through point a (3,0) and intersects with Y-axis at point B, if the area of triangle AOB is 6, the analytic expression of the first-order function is obtained

Let the coordinate of the intersection B be (0, m), and the analytic formula of the first-order function be y = KX + B
The area of the triangle is 6
1 / 2 * 3 * | m | = 6
We get that | m | = 4
If M = 4, then the coordinate of point B is (0,4)
Substituting points a and B into the analytic expression of the function respectively, there is 3K + B = 0, expression 1
B = 4 equation 2
K = - 4 / 3, B = 4
Then the analytic expression of the linear function is y = - 4x / 3 + 4
If M = - 4, then the coordinates of point B are (0, - 4)
Substituting points a and B into the analytic expression of the function respectively, there is 3K + B = 0, expression 1
B = - 4, equation 2
K = 4 / 3, B = - 4
Then the analytic expression of the first-order function is y = 4x / 3-4
In conclusion, the analytic expression of the first-order function is y = - 4x / 3 + 4 or y = 4x / 3-4

Function f (x) = 2x + 2, X ∈ [- 1,0], = - 1 / 2x, X ∈ [0,2], = 3x, X ∈ [2, + ∞) to find the definition and range of function
Function f (x) = 2x + 2, X ∈ [- 1,0),
=-1/2x,x∈[0,2),
=The definition and range of 3x, X ∈ [2, + ∞)

Domain [- 1, + ∞)
Range [6, + ∞) ∪ [- 1,2)

Cut the cuboid which is 60cm long into three sections, and the surface area increases by 180cm square. What is the original volume of the cuboid?
List the formulas

Bottom area = 180 △ 4 = 45 square centimeter
Volume = 45 × 60 = 2700 CC

Let the equation 1 / 3x ^ 3-x ^ 2-3x + a = 0 have three unequal real roots, then the value range of real number a is

Let f (x) = 1 / 3x ^ 3-x ^ 2-3x + A, then: F '(x) = x ^ 2-2x-3, we know that the vertex coordinates of F' (x) are (1, - 4), and △ > 0, and X1 = 3, X2 = - 1, so f (x) is an increasing function in (negative infinity, - 1), (- 1,3) is a decreasing function, and (3, positive infinity) is an increasing function, because the equation has three unequal real roots

If a and B are opposite to each other, C and D are reciprocal to each other, the absolute value of M = 3
Find a + B + MCD + M

If a and B are opposite numbers, C and D are reciprocal numbers, | m | = 3, a ≠ 0; find (a + b) / M + MCD + B / A. analysis: A and B are opposite numbers, a + B = 0, B / a =? 1; C and D are reciprocal numbers, CD = 1; | m | = 3, M = ± 3; 1. When m = + 3, (a + b) / M + MCD + B / a = 0 + 3? 1 = 2; 2. When m =? 3, (a + b) / M + MCD + B / a = 0? 1 =? 4

Given that the function f (x) = x / (AX + b), (a, B are constants, and ab ≠ 0), and f (2) = 1, f (x) = x has a unique solution, then the analytic expression of y = f (x) is? There are several cases
Given that the function f (x) = x / (AX + b), (a, B are constants, and ab ≠ 0), and f (2) = 1, f (x) = x has a unique solution, then the analytic expression of y = f (x) is?
F (x) = x / (AX + b) = x, x = x (AX + b), X (AX + B-1) = 0, obviously x = 0 is a solution, so the solution of AX + B-1 = 0 is also x = 0, x = (1-B) / a = 0, B = 1, a = 1 / 2, which is the answer on the Internet, but I think we should also consider the case of increasing roots!
Here's another answer:
That is, X / (AX + b) = x, movable term, general division, to ensure that the denominator is not zero, x = 0 or a / (1-B), but it should also be satisfied that x is not equal to - A / B, so in addition to the above situation, it is possible that - A / b = 0, and rounding off, it is only one X = A / (1-B). At this time, B = 0, a = 1, is it also in line with the meaning? Therefore, I think the result should have two cases!

If f (2) = 1 so f (2) = 2 / 2A + B = 1, then 2A + B = 2 -------- 1
F (x) = x / ax + B = x, that is, ax ^ 2 + (B-1) x = 0 has a unique solution! That is, a quadratic function has a unique solution
So △ = (B-1) ^ 2 = 0, so B = 1 brings B = 1 into formula a = 1 / 2
(x ^ 2 for square)
I'm sure it's right