Question
Download Solution PDFयदि x + \(\frac{1}{2x}\) = 3 है, तो 8x3 + \(\rm \frac{1}{x^3}\) का मान क्या है?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFदिया 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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