Question

The total number of values of x satisfying x² – 3|x| + 2 = 0 is ______.

Answer 1

The total number of values of x satisfying x² – 3|x| + 2 = 0 is 4.

Explanation:

Let t = |x| (t ≥ 0).

Then t² – 3t + 2 = 0 

⇒ (t – 1)(t – 2) = 0

So t = 1 or t = 2. 

Thus |x| = 1 ⇒ x = ±1 (2 values) and |x| = 2 ⇒ x = ±2 (2 values). 

Total values of x = 2 + 2 = 4.