Question
Download Solution PDFयदि \(a + \frac{1}{a} = 7\) है, तो \(a^5 + \frac{1}{a^5} \) का मान निम्नलिखित में से किसके बराबर है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया गया है:
\(a + \frac{1}{a} = 7\)
प्रयुक्त सूत्र:
(a + 1/a) = P ; तब
(a2 + 1/a2) = P2 - 2
(a3 + 1/a3) = P3 - 3P
\(a^5 + \frac{1}{a^5} \) = (a2 + 1/a2) × (a3 + 1/a3) - (a + 1/a)
गणना:
a + (1/a) = 7
⇒ (a2 + 1/a2) = (7)2 - 2 = 49 - 2 = 47
⇒ (a3 + 1/a3) = (7)3 - (3 × 7) = 343 - 21 = 322
a5 + (1/a5) = (a2 + 1/a2) × (a3 + 1/a3) - (a + 1/a)
⇒ 47 × 322 - 7
⇒ 15134 - 7 = 15127
∴ सही उत्तर 15127 है।
Last updated on Jun 13, 2025
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