solve for x: x(x²-4) ≤0
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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.
- x = 0
- (x + 2) = 0 ⇒ x = -2
- (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]
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