यदि (x2 + \(\frac{1}{x^2}\)) = 18, और x > 0 है, तो (x3 + \(\frac{1}{x^3}\)) का मान क्या है?

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SSC CGL 2023 Tier-I Official Paper (Held On: 21 Jul 2023 Shift 4)
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  1. 36\(\sqrt5\)
  2. 40\(\sqrt5\)
  3. 46\(\sqrt5\)
  4. 34\(\sqrt5\)

Answer (Detailed Solution Below)

Option 4 : 34\(\sqrt5\)
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Detailed Solution

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गणना:

x2 + 1 / x2 = 18

(X + 1 / X)2 = 18 +2

= 20

x+1/x = 2√5

 (x3 + \(\frac{1}{x^3}\)) = (x+1/x)3 - 3 (x+1/x)

⇒ 40√5 - 6√5

= 34\(\sqrt5\)

∴ सही विकल्प 4 है।

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