Question
Download Solution PDFIf
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
x + 1/x = 2√2
Formula used:
If x + 1/x = n
then, x2 + 1/x2 = n2 - 2
And (a + b)3 = a3 + b3 + 3ab (a + b)
Calculation:
x + 1/x = 2√2
⇒ x2 + 1/x2 = (2√2)2 - 2
⇒ x2 + 1/x2 = 6
Cubing both side we get
⇒ (x2 + 1/x2)3 = 63
⇒ x6 + 1/x6 + 3 (x2 × 1/x2) (x2 + 1/x2) = 63
⇒ x6 + 1/x6 + 3 × 1 × 6 = 63
⇒ x6 + 1/x6 = 63 - 3 × 6
⇒ x6 + 1/x6 = 216 - 18
⇒ x6 + 1/x6 = 198
∴ The value of x6 + 1/x6 is 198.
Last updated on Jul 22, 2025
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