Question:
If \(x – \dfrac{1}{x} = 2\), find the value of \(x^4 + \dfrac{1}{x^4}\).
यदि \(x – \dfrac{1}{x} = 2\) है, तो \(x^4 + \dfrac{1}{x^4}\) का मान ज्ञात कीजिए।
Options:
- 18
- 34
- 14
- 20
- 18
- 34
- 14
- 20
Correct Answer: b)
Explanation:
Squaring \(x – \dfrac{1}{x} = 2\):
\(x^2 + \dfrac{1}{x^2} – 2 = 4 \implies x^2 + \dfrac{1}{x^2} = 6\).
Squaring again:
\(x^4 + \dfrac{1}{x^4} + 2 = 36 \implies x^4 + \dfrac{1}{x^4} = 34\).
\(x – \dfrac{1}{x} = 2\) का दोनों तरफ वर्ग करने पर:
\(x^2 + \dfrac{1}{x^2} – 2 = 4 \implies x^2 + \dfrac{1}{x^2} = 6\)।
पुनः वर्ग करने पर:
\(x^4 + \dfrac{1}{x^4} + 2 = 36 \implies x^4 + \dfrac{1}{x^4} = 34\)।