Exams › SSC CGL (Prelims) › General

If \(x + \frac{1}{x} = 5\), then find the value of \(x^3 + \frac{1}{x^3}\).

1. 110
2. 125
3. 140
4. 115

Correct answer: 110

Solution

Using \((x + \frac{1}{x})^3 = x^3 + \frac{1}{x^3} + 3\left(x + \frac{1}{x}\right)\), substitute the given value 5. First, \(x^2 + \frac{1}{x^2} = 5^2 - 2 = 23\), so \(x^3 + \frac{1}{x^3} = 5^3 - 3\cdot 5 = 110\).

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