Exams › SSC CGL (Prelims) › General

Given \(x + \frac{1}{x} = 5\), find \(x^3 + \frac{1}{x^3}\).

1. 100
2. 110
3. 120
4. 125

Correct answer: 110

Solution

Let \(a = x + \frac{1}{x} = 5\). Then \(x^3 + \frac{1}{x^3} = a^3 - 3a\). Substituting \(a=5\) gives \(125 - 15 = 110\).

Related SSC CGL (Prelims) General questions

• If $3x + 7 = 28$, find $x$.
• Simplify: \((15 + \sqrt{3}) + (15 - \sqrt{3}) - (1025 - 3)\)
• If $t=\sqrt{6}+3$, find $t^2-6\sqrt{6}$.
• If \(m + \frac{1}{m} = 6\), find the value of \(m^2 + \frac{1}{m^2}\).
• If $7x + 5 = 61$, then $x = ?$
• Find the y-intercept of \(5x + 3y = 15\).

⚔️ Practice SSC CGL (Prelims) General free + battle 1v1 →