Question

Prove that: (x+1÷x^2)^2-2=x^4+1÷x^4​

Answer 1

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(x - 1/x) = 2

[ on SQUARING both side]

we get,

=> x² + 1/x² - 2×x×1/x = 4

=> x² + 1/x² = 4 +2

=> (x² + 1/x²) = 6

[again squaring on both side]

we get,

x⁴ + 1/x⁴ + 2×x² ×1/x² = 6²

=> (x⁴ + 1/x⁴) = 36 - 2

=> (x⁴ + 1/x⁴) = 34