Question

${\displaystyle \frac{2}{x^2}-\frac{5}{x}+2}$ = 0

Answer 1

${\displaystyle \frac{2}{x^2}-\frac{5}{x}+2}$ = 0

⇒ ${\displaystyle \frac{2-5x+2x^2}{x^2}}$ = 0
⇒ 2x² - 5x + 2 = 0
⇒ 2x² - 4x - x + 2 = 0
⇒ 2x(x - 2) -1(x -2) = 0
⇒ (x - 2)(2x - 1) = 0
⇒ x - 2 = 0 or 2x - 1 = 0

⇒ x = 2 or x = ${\displaystyle \frac{1}{2}}$ are two root of the equation.