Question

Решите неравенство:(x²+2x)(4x-2)>0​

Answer 1

Ответ:

x принадлежит (-2;0) и (1/2 до +бесконечности)

Объяснение:

решаем систему уравнений

x^2+2x>0

4x-2>0

Answer 2

To solve this inequality, we need to find the values of x that make the left-hand side greater than zero. We can start by factoring the left-hand side:

(x² + 2x)(4x - 2) = 2x(x + 2)(2x - 1)

Now we can see that the left-hand side will be greater than zero if either:

1. 2x > 0 and (x + 2) > 0 and (2x - 1) > 0
2. 2x < 0 and (x + 2) < 0 and (2x - 1) < 0

Simplifying these conditions, we get:

1. x > 0 and x > -2 and x > 1/2 (or x > 2 since x must be greater than 1/2)
2. x < 0 and x < -2 and x < 1/2

So the solution to the inequality is:

x < -2 or 0 < x < 1/2 or x > 2

In interval notation, we can write the solution as:

(-∞, -2) ∪ (0, 1/2) ∪ (2, +∞)