m2 – 3m – 1 = 0

(iii) m² – 3m – 1 = 0 

Sol. m² – 3m – 1 = 0

∴  m² – 3m = 1 .... (i)

Third term = ( ½ ×  coefficient of m)²

= ( ½ × - 3)²

= (^-3/₂)²

= ⁹/₄

Adding ⁹/₄ to both sides of (i), we get,

 m² – 3m + ⁹/₄ = 1+ ⁹/₄ .... (i)

∴ (m – ³/₂)² = ¹³/₄

∴ (m – ³/₂) = ± √(¹³/₄)

∴ m – ³/₂ = ± ^√13 /₂

∴ m = ³/₂ ± ^√13/₂

∴ m = ^(3±√13)/₂

∴ m = ^(3+√13)/₂  or  ^{(3 - √13)}/₂