Question
Download Solution PDFयदि \(\rm\left(x + \frac{1}{x}\right)\) = 2√2 है, तो \(\rm\left(x^{6}+\frac{1}{x^{6}}\right)\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
x + 1/x = 2√2
प्रयुक्त सूत्र:
यदि x + 1/x = n
तब, x2 + 1/x2 = n2 - 2
और (a + b)3 = a3 + b3 + 3ab (a + b)
गणना:
x + 1/x = 2√2
⇒ x2 + 1/x2 = (2√2)2 - 2
⇒ x2 + 1/x2 = 6
दोनों पक्षों का घन करने पर, हमें प्राप्त होता है,
⇒ (x2 + 1/x2)3 = 63
⇒ x6 + 1/x6 + 3 (x2 × 1/x2) (x2 + 1/x2) = 63
⇒ x6 + 1/x6 + 3 × 1 × 6 = 63
⇒ x6 + 1/x6 = 63 - 3 × 6
⇒ x6 + 1/x6 = 216 - 18
⇒ x6 + 1/x6 = 198
∴ x6 + 1/x6 का मान 198 है।
Last updated on Jun 25, 2025
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