Let m ∈ R be an inequality m ^ 2x ^ 2 + 2mx-2 about X

Sub situation:
1. M = 0, get - 20, opening upward, as long as △ 0, go to the middle part
△ = 4m ^ 2-4m ^ 2 * (- 2) = 12m ^ 2 constant > 0
Solve the two roots of m ^ 2x ^ 2 + 2mx-2 = 0, x1, X2, expressed by M
So x1

Find the solution of the inequality M2X + 2 ＞ 2mx + m about X

The original inequality can be changed into: m (m-2) x ＞ m-2 (1) when m-2 ＞ 0 is m ＞ 2, MX ＞ 1, the solution of inequality is x ＞ 1m (2) when m-2 ＜ 0 is m ＜ 2, MX ＜ 1. When 0 ＜ m ＜ 2, the solution of inequality is x ＜ 1m; when m ＜ 0, the solution of inequality is x ＞ 1m; when m = 0, the solution of inequality is all real numbers

RELATED INFORMATIONS

1. When x > 3, the inequality x + 1 / (x-1) - a ≥ 0 holds, and the value range of real number a is obtained
2. Given that the function F X = x2-2ax + 3A + 1 decreases monotonically on (- ∞, 1), then the value range of real number a is
3. Why does the function y = loga (1-2x) monotonically increase by 0 on the domain of definition
4. The function f (x) = 2Sin (2x + (π / 6)) + A is known, where a is a constant Finding monotone decreasing interval of F (x) When x ∈ [0, π / 2], the maximum value of F (x) is 4
5. Given that the function f (x) = 2Sin ω x monotonically decreases on [- π 4, π 4], then the value range of real number ω is______ ．
6. Given that w is a positive real number and the function f (x) = 2sinwx is an increasing function on [- Pai / 3, Pai / 3], then the value range of W is Given that w is a positive real number and the function f (x) = 2sinwx is an increasing function on [- Pai / 3, Pai / 3], then the value range of W is 3 / 2], can't understand the analysis in the book, Y = 2sinwx is an increasing function on [- Pai / 2, Pai / 2]. To make FX = sinwx an increasing function on [- Pai / 3, Pai / 3], we only need t / 2 > = Pai / 3 - (- Pai / 3) = 2 Pai / 3, that is, 2 Pai / W > = 4 Pai / 3, so the answer is as above
7. Find the monotone increasing interval of function f (x) = 3sin (x / 2 + π / 6) + 3
8. The function f (x) = sin (x + α) + √ 3cos (x - α) is known, where 0 ≤ α < π and f (x) = f (- x) is constant for any real number X (1) Finding the value of α (2) Finding the maximum value and monotone increasing interval of function f (x)
9. A is an internal angle of a triangle, the square of function y = x times cosa-4sina + 6, for any x belongs to R, y is greater than 0!
10. If the function y = 2cos (2x + φ) is odd and is an increasing function on (0, π / 4), then the real number φ may be () A. - π / 2 b.0 C. π / 2 d. π
11. Given the function f (x) = - x2 + ax + b2-b + 1, (a, B ∈ R), f (1-x) = f (1 + x) holds for any real number X. if f (x) > 0 holds for X ∈ [- 1, 1], then the value range of B is () A. - 1 ＜ B ＜ 0b. B ＞ 2C. B ＞ 2 or B ＜ - 1D. B ＜ - 1
12. If a, B and C are three sides of △ ABC, and a and B satisfy the relation | A-3 | + (B-4) + 0, C is a system of inequalities x-3 / 3 > x-4,2x + 3x-4,2x + 3
13. If ABC is three sides of the triangle ABC, and ab satisfies the relation | A-3 | + B ^ 2-8b + 16 = 0, C is the minimum integer solution of the inequality system, and the shape of the triangle ABC is judged The inequality system X-1 / 3 > x + 4 of C 2x+3
14. Given that f (x) is a quadratic function, the solution set of inequality f (x) less than 0 is (0,5), and f (x) has a maximum value of 12 on {- 1,4], the analytic expression of F (x) is obtained Second question: is there a natural number m such that the equation f (x) + 37 / x = 0 has only two unequal real roots in the interval (m, M + 1)?
15. It is known that positive integers, N, K satisfy the inequality 6 / 11 ＜ n / K ＜ 5 / 9, then when n and K take the minimum value, the value of N + k is?
16. The sum of all natural numbers n suitable for inequality 718 < N5 < 207 is______ ．
17. Set 0
18. If f (x) = 9 to the x power and (K + 1) 3 to the x power + 1 > 0 holds, then the range of K is
19. Given the function f (x) = xlnx, if f (x) > = AX-1 holds for any x > 0, then the value range of a is a = 1
20. Let f (x) = xlnx, X ∈ [e ^ - 2, e], then the maximum value of F (x) is