x (x – 1) = 1

(vi) x (x – 1) = 1

Sol. x (x – 1) = 1

∴  x² – x = 1 .... (i)

Third term = ( ½ ×  coefficient of x)²

= ( ½ × - 1)²

= (- ½ )²

= ¼

Adding ¼  to both sides of (i), we get,

∴  x² – x + ¼ = 1 + ¼

∴ (x – ½ )² = 5/4

∴ (x – ½) = ±√⁵/₄

∴ x + ½ = ± ^√5/₂

∴ x = - ½ ± ^√5/₂

∴ x = ^{(- 1 + √5)/}₂   or ^{(-1 - √5)}/₂