Question

solve for x: x(x²-4) ≤0​

Answer 1

Answer :-

x ∈ (-∞, -2] U (0, 2]

Step-by-step explanation :-

Given inequality → x (x² - 4) ≤ 0

Here, using the identity (a + b) (a - b) = a² - b²

(x² - 4) can be written as → (x + 2) (x - 2).

So, the given inequality becomes

x (x + 2) (x - 2) ≤ 0

Now solve by drawing a Wavy curve for this.

(refer attachment)

Finding the break points:

There are 3 terms and so there would be 3 break points for the inequality.

1. x = 0
2. (x + 2) = 0 ⇒ x = -2
3. (x - 2) = 0 ⇒ x = 2

After plotting the points, we consider only the negative part because the given inequality is less than or equal to zero.

Hence,

The value of x ∈ (-∞, -2] U (0, 2]