Question

Solve the following equation by factorization:

`10x - 1/x = 3`

Answer 1

Given,

⇒ `10x - 1/x = 3`

⇒ `(10x^2 - 1)/x = 3`

⇒ 10x² – 1 = 3x

⇒ 10x² – 3x – 1 = 0

⇒ 10x² – 5x + 2x – 1 = 0

⇒ 5x(2x – 1) + 1(2x – 1) = 0

⇒ (5x + 1)(2x – 1) = 0

⇒ (5x + 1) = 0 or (2x – 1) = 0   ...[Using zero-product rule]

⇒ 5x = –1 or 2x = 1

⇒ `x = -1/5` or `x = 1/2`

Hence, `x = {1/2, -1/5}`.