Question

Solve the following equation by using formula:

`x - (1)/x = 3, x ≠ 0`

Answer 1

`x - (1)/x = 3`

x² – 1 = 3x

⇒ x² – 3x – 1 = 0

Here a = 1, b = -3, c = -1

∴ b² - 4ac

= (-3)² - 4 × 1 × (-1)

= 9 + 4

= 13

x = `(-b ± sqrt(b^2 - 4ac))/(2a)`

= `(-(-3) ± sqrt(13))/(2 xx 1)`

= `(3 ± sqrt(13))/(2)`

∴ x = `(3 + sqrt(13))/(2) and (3 - sqrt(13))/(2)`.