Question:
If \(x + \frac{1}{x} = 4\), find the value of \(x^3 + \frac{1}{x^3}\).
यदि \(x + \frac{1}{x} = 4\) है, तो \(x^3 + \frac{1}{x^3}\) का मान ज्ञात कीजिए।
Options:
- 52
- 64
- 48
- 56
- 52
- 64
- 48
- 56
Correct Answer: a)
Explanation:
Using the identity: \(x^3 + \frac{1}{x^3} = \left(x + \frac{1}{x}\right)^3 – 3\left(x + \frac{1}{x}\right)\)
\(= 4^3 – 3(4) = 64 – 12 = \textbf{52}\) (Option a).
सर्वसमिका: \(x^3 + \frac{1}{x^3} = (x + \frac{1}{x})^3 – 3(x + \frac{1}{x}) = 4^3 – 3(4) = 64 – 12 = \textbf{52}\) (विकल्प a)।