If x + 1 / x = 4 ,Find x⁴ + 1 / x
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Answer: x + 1/x = 4
Squaring both sides,
(x + 1/x)² = 4²
x² + 1/x² + 2×x×1/x = 16
x² + 1/x² + 2 = 16
x² + 1/x² = 14
Now, again squaring both sides,
(x² + 1/x²)² = 14²
x⁴ + 1/x⁴ + 2×x²×1/x² = 196
x⁴ + 1/x⁴ + 2 = 196
∴ x⁴ + 1/x⁴ = 194
Step-by-step explanation:
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