Find the number of real solutions of x² - 5|x| + 6 = 0 — JEE Mathematics

Let $|x| = y$. Since $x^2 = |x|^2 = y^2$, rewrite the equation as:

$$y^2 - 5y + 6 = 0 \implies (y-2)(y-3) = 0 \implies y = 2 or y = 3$$

Since $y = |x|$:

• $|x| = 2 \implies x = \pm 2$
• $|x| = 3 \implies x = \pm 3$

There are 4 distinct real solutions: $-3, -2, 2, 3$.

Answer: 4