If x + 1/x = √2, determine the value of x⁶ + 1/x⁶.
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Correct answer: D
Explanation
Given,
x + 1/x = √2
Squaring both sides,
x² + 1/x² + 2 = 2
x² + 1/x² = 0
(x² + 1/x²)³ = x⁶ + 1/x⁶ + 3(x² + 1/x²)
0 = x⁶ + 1/x⁶ + 0
x⁶ + 1/x⁶ = 0