यदि x + \(\frac{1}{2x}\) = 3 है, तो 8x3\(\rm \frac{1}{x^3}\) का मान क्या है?

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SSC CGL 2022 Tier-I Official Paper (Held On : 05 Dec 2022 Shift 4)
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  1. 212
  2. 216
  3. 180
  4. 196

Answer (Detailed Solution Below)

Option 3 : 180
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PYST 1:SSC CGL 2023 - Quantitative Aptitude(Held On:14 Jul 2023 Shift 1)
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दिया गया:

x + \(\frac{1}{2x}\) = 3

प्रयुक्त अवधारणा:

सरल गणनाओं का प्रयोग किया जाता है

गणना:

⇒ x + \(\frac{1}{2x}\) = 3

दोनों पक्षों में 2 का गुणा करने पर, हमें प्राप्त होता है

⇒ 2x + \(\frac{1}{x}\) = 6  .................(1)

अब, दोनों पक्षों को घन करने पर,

⇒ \((2x + \frac{1}{x})^3 = 6^3\)

⇒ \(8x^3 + \frac{1}{x^3} + 3(4x^2)(\frac{1}{x})+3(2x)(\frac{1}{x^2})=216\)

⇒ \(8x^3 + \frac{1}{x^3} + 12x+\frac{6}{x}=216\)

⇒ \(8x^3 + \frac{1}{x^3}= 216 - 6(2x+\frac{1}{x})\)

⇒ \(8x^3 + \frac{1}{x^3}= 216- 6(6)\)  ..............(1) से 

⇒ \(8x^3 + \frac{1}{x^3}= 216- 36\)

⇒ \(8x^3 + \frac{1}{x^3}= 180\)

इसलिए, उपरोक्त समीकरण का मान 180 है।

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