Question
If (x - 1/x)2 = 3, then the value of
x6 + 1/x6 equalsSolution
(x – 1/x)2 = 3 => (x2 + 1/x2) – 2 = 3 (x2 + 1/x2) = 5 ∵ and we know that if (x + 1/x) = a then (x3 + 1/x3) = a3 – 3a => (x2 + 1/x2) = 5 => (x6 + 1/x6) = (5)3 – 3 × 5 = 110
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