Question
Download Solution PDFIf \(\rm \left(x-\frac{1}{x}\right)=2\sqrt2\), what is the value of \(\rm \left(x^6+\frac{1}{x^6}\right) \)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula Used:
(a + b)2 = a2 + b2 + 2ab
(a + b)3 = a3 + b3 + 3ab(a + b)
Calculation:
As per the question,
x - 1/x = 2√2
⇒ (x - 1/x)2 = 8
⇒ (x2 + 1/x2) = 10
Again,
(x2 + 1/x2)3= \(\rm \left(x^6+\frac{1}{x^6}\right) \) + 3(x2 + 1/x2 )
x6 + 1/x6 = (10)3 - 3(10)
x6 + 1/x6 = 1000 - 30 = 970
∴ The correct option is 4
Last updated on Jul 7, 2025
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