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  

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