Question
Download Solution PDFIf x + \(\frac{1}{2x}\) = 3, then evaluate 8x3 + \(\rm \frac{1}{x^3}\).
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x + \(\frac{1}{2x}\) = 3
Concept Used:
Simple calculations is used
Calculations:
⇒ x + \(\frac{1}{2x}\) = 3
On multiplying 2 on both sides, we get
⇒ 2x + \(\frac{1}{x}\) = 6 .................(1)
Now, On cubing both sides,
⇒ \((2x + \frac{1}{x})^3 = 6^3\)
⇒ \(8x^3 + \frac{1}{x^3} + 3(4x^2)(\frac{1}{x})+3(2x)(\frac{1}{x^2})=216\)
⇒ \(8x^3 + \frac{1}{x^3} + 12x+\frac{6}{x}=216\)
⇒ \(8x^3 + \frac{1}{x^3}= 216 - 6(2x+\frac{1}{x})\)
⇒ \(8x^3 + \frac{1}{x^3}= 216- 6(6)\) ..............from (1)
⇒ \(8x^3 + \frac{1}{x^3}= 216- 36\)
⇒ \(8x^3 + \frac{1}{x^3}= 180\)
⇒ Hence, The value of the above equation is 180
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