If x4 + x-4 = 2599, then one of the values of x – x-1, where x > 0, is equal to:
If x4 + x-4 = 2599, then one of the values of x – x-1, where x > 0, is equal to: Correct Answer 7
x4 + x-4 = 2599
As we know,
(x2 + 1/x2)2 = x4 + 1/x4 + 2
⇒ (x2 + 1/x)2 = 2599 + 2 = 2601
⇒ (x2 + 1/x2) = √2601 = 51
Again, (x – 1/x)2 = x2 + 1/x2 – 2
⇒ (x – 1/x)2 = 51 – 2 = 49
⇒ x – x-1 = √49 = 7
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Feb 20, 2025