Correct Answer - Option 4 : 322
Given:
\(x + {1 \ \over x} = 7\)
Formula used:
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:
As, \(x + {1 \ \over x} = 7\)
Cubing equation we get,
\( {x^3 \ } + {1 \ \over x^3}\) + 3 × 7 = 343
\( {x^3 \ } + {1 \ \over x^3}\) = 343 - 21 = 322
∴ The value of \( {x^3 \ } + {1 \ \over x^3}\) is 322