Question
Download Solution PDFयदि x + \(\frac{1}{x}\) = 7 है, तो x6 + \(\frac{1}{x^6}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
x + 1/x = 7
प्रयुक्त सूत्र:
यदि x + 1/x = n
तब, x 2 + 1/x 2 = n 2 - 2
और (x 3 + y 3) = n 3 - 3n
गणना:
x + 1/x = 7
⇒ x 2 + 1/x 2 = 7 2 - 2
⇒ x 2 + 1/x 2 = 47
दोनों पक्षों का घन करने पर हमें प्राप्त होता है
⇒ (x2 + 1/x2) 3 = 47 3
⇒ x 6 + 1/x 6 + 3 (x2 × 1/x2) (x2 + 1/x2) = 47 3
⇒ x6 + 1/x6 + 3 × 1 × 47 = 473
⇒ x6 + 1/x6 = 473 - 3 × 47
⇒ x 6 + 1/x 6 = 103823 - 141
⇒ x 6 + 1/x 6 = 103682
∴ x 6 + 1/x 6 का मान 103682 है।
Last updated on Jul 19, 2025
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