यदि x + \(\frac{1}{x}\) = 7 है, तो x6\(\frac{1}{x^6}\) का मान क्या है?

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SSC CGL 2023 Tier-I Official Paper (Held On: 14 Jul 2023 Shift 3)
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  1. 113682
  2. 103682
  3. 103882 
  4. 103862

Answer (Detailed Solution Below)

Option 2 : 103682
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दिया 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।

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