Bihar Police Constable Model Paper 1

Given:
x – 1/x = 4
Formula used:
${\left(\mathit{a}\mathit{–}\mathit{b}\right)}^3$ = ${\mathit{a}}^3\mathit{–}{\mathit{b}}^3$ – 3ab(a – b)
Calculation:
Our given expression is x – 1/x = 4
Taking cube on both the sides,
${\left(\mathit{x}\mathit{–}\frac{1}{\mathit{x}}\right)}^3$ = 43
⇒ ${\mathit{x}}^3\mathit{–}\frac{1}{{\mathit{x}}^3}$ – 3x × 1/x(x – 1/x) = 64
⇒ ${\mathit{x}}^3\mathit{–}\frac{1}{{\mathit{x}}^3}$ – 3 × 4 = 64 ----(∵ x – 1/x = 4)
⇒ ${\mathit{x}}^3\mathit{–}\frac{1}{{\mathit{x}}^3}$ = 64 + 12
⇒ ${\mathit{x}}^3\mathit{–}\frac{1}{{\mathit{x}}^3}$ = 76
∴ The value of the given expression is 76