Question

Solve the following equation by factorization:

`x + 1/x = 3 1/3, x ≠ 0`

Answer 1

Given,

⇒ `x + 1/x = 3 1/3`

⇒ `(x^2 + 1)/x = (9 + 1)/3`

⇒ `(x^2 + 1)/x = 10/3`

⇒ 3 × (x² + 1) = 10x

⇒ 3x² + 3 = 10x

⇒ 3x² – 10x + 3 = 0

⇒ 3x² – 9x – x + 3 = 0

⇒ 3x(x – 3) – 1(x – 3) = 0

⇒ (x – 3)(3x – 1) = 0

⇒ x – 3 = 0 or 3x – 1 = 0   ...[Using zero-product rule]

⇒ x = 3 or 3x = 1

⇒ x = 3 or x = `1/3`

Hence, `x = {3, 1/3}`.