Question

Solve the following equation by factorization

`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`

Answer 1

`(2)/(x^2) - (5)/x + 2 = 0, x ≠ 0`
⇒ 2 - 5x + 2x² = 0
⇒ 2x² - 5x + 2 = 0    ...`{(∵ 2 xx 2 = 4),(4 = -4 xx (-1)),(-5 = -4 - 1):}}`
⇒ 2x² - 4x - x + 2 = 0
⇒ 2x(x - 2) - 1(x - 2) = 0
⇒ (x - 2) (2x - 1) = 0
Either x - 2 = 0,
then x = 2
or 
2x = 1 = 0,
then 2x = 1

⇒ x = `(1)/(2)`

∴ x = 2, `(1)/(2)`.