If the function f (x) = 2ax2-x-1 has exactly one zero point in (0,1), then the value range of a is () A. （1，+∞）B. （-∞，-1）C. （-1，1）D. [0，1）

If the function f (x) = 2ax2-x-1 has exactly one zero point in (0,1), then the value range of a is () A. （1，+∞）B. （-∞，-1）C. （-1，1）D. [0，1）

When △ = 0, a = - 18, there is a zero point x = - 2, which is not on (0, 1), so it does not hold. The function f (x) = 2ax2-x-1 has exactly a zero point in (0, 1), that is, f (0) f (1) < 0, that is - 1 × (2a-1) < 0. The solution is a > 1, so a is selected

On the inequality of X | x-4 | - | x-3|

Both minus sign and plus sign transform the absolute value function into a piecewise function to find the value range of the absolute value function. When calculating the value range, pay attention to the value range of X. The definition field is divided into three sections by 3 and 4. Then the function image y = a is not an empty set on the minimum value of the image y = | x-4 | - | x-3 |

Factorization of 18x ^ 3Y ^ 2-2x ^ 3

Original form
=2x³(9y²-1)
=2x³(3y+1)(3y-1)

Given u = {- 1,1}, set a = {x ∈ u x ^ 2-ax + 1 = 0}, if CUA = u, then the set range of real number a is

U = {- 1,1}, set a = {x ∈ u | x ^ 2-ax + 1 = 0},
∵CuA=U
∴A=Φ
When Δ = a ^ 2-4 - 2

How to find the minimum value of function x + 1 / 2x

The square term is constant and nonnegative, x ^ 2 ≥ 0, x ^ 2 + 1 > 0, the denominator is always meaningful, and the definition field is r
Let y = 2x / (x ^ 2 + 1)
yx^2-2x +y=0
The equation has solution and the discriminant is ≥ 0
(-2)^2-4y^2≥0
y^2≤1
-1≤y≤1
The minimum value of 2x / (x ^ 2 + 1) is - 1, and the maximum value is 1. When the minimum value is taken, x = - 1

It is known that the vertex of the parabola is (3, - 2), and the distance between the two intersections of the parabola and the X axis is 4
Finding quadratic function

y=0.5*(x-1)*(x-5).

If the product of five rational numbers is negative, then the number of positive factors in the five rational numbers is ()
A. 0 or 2 b. 1 or 3 C. 0 or 2 or 4 d. 1 or 3 or 5

The product of five rational numbers is negative, the number of negative factors is 1 or 3 or 5, and the number of positive factors is 4 or 2 or 0

The process and answer of 6x-7 = 4x-5

Because 6x-7 = 4x-5
So (6x-7) - (4x-5) = 0
So 2x-2 = 0
So 2x = 2
So x = 1

If the square of the difference between the two of x2-5x + k = 0 is 16, then K=______

From the meaning of the question, we can see that X1 + x2 = 5, x1x2 = k, (x1-x2) 2 = (x1 + x2) 2-4x1x2 = 25-4k = 16, ｜ k = 94

Given the circle X & # 178; + Y & # 178; - 6mx-2 (m-1) y + 10m-2m-24 = 0 (m ∈ R), the center of the circle is on the straight line L, the equation of L is solved

x²+y²-6mx-2(m-1)y+10m²-2m-24=0
(x-3m)^2+[y-(m-1)]^2=25
So the center of the circle is (3m, m-1)
So the trajectory equation is y = x / 3 - 1