Dehli Police Constable Model Paper 2 (HM)

दिया है​​:
$\mathit{x}+\frac{1}{\mathit{x}}$ = 4
उपयोग किया गया सूत्र:
${\mathit{x}}^2+\frac{1}{{\mathit{x}}^2}$ = ${\left(\mathit{x}+\frac{1}{\mathit{x}}\right)}^2$ - 2
गणना:
मान ले संख्या = x
$\mathit{x}+\frac{1}{\mathit{x}}$ = 4
⇒ ${\left(\mathit{x}+\frac{1}{\mathit{x}}\right)}^2$ = $4^2$ = 16
⇒ ${\mathit{x}}^2+\frac{1}{{\mathit{x}}^2}+2$ = 16
⇒ ${\mathit{x}}^2+\frac{1}{{\mathit{x}}^2}$ = 14
अब,
$\left(\mathit{x}+\frac{1}{\mathit{x}}\right)\left({\mathit{x}}^2+\frac{1}{{\mathit{x}}^2}\right)$ = 4 × 14
⇒ ${\mathit{x}}^3+\frac{1}{\mathit{x}}+\mathit{x}+\frac{1}{{\mathit{x}}^3}$ = 56
⇒ ${\mathit{x}}^3+\frac{1}{{\mathit{x}}^3}+\mathit{x}+\frac{1}{\mathit{x}}$ = 56
⇒ ${\mathit{x}}^3+\frac{1}{{\mathit{x}}^3}+4$ = 56
⇒ ${\mathit{x}}^3+\frac{1}{{\mathit{x}}^3}$ = 52
स्मार्ट ट्रिक
अगर x + 1/x = a, तो ${\mathit{x}}^3+\frac{1}{{\mathit{x}}^3}$ = ${\mathit{a}}^3\mathit{–}3\mathit{a}$
यहाँ, a = 4,
∴ ${\mathit{x}}^3+\frac{1}{{\mathit{x}}^3}$ = $4^3$ - 3 × 4 = 64 – 12 = 52.