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If \(x + {1 \ \over x} = 7\) then the value of \( {x^3 \ } + {1 \ \over x^3}\)
1. 343
2. 341
3. 352
4. 322

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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

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