18. If x +1/x = 2, prove that x² + 1/x2 = x3+ 1/x = x4+1/x4 . Created by yashraj2401u.

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September 2023 1 8 Report

18. If x +1/x = 2, prove that x² + 1/x2 = x3+ 1/x = x4+1/x4

Step-by-step explanation:

x + 1/x = 2 => x² +1 = 2x

=> x²-2x + 1 =0 => (x-1)²= 0

=>. x = 1

for x=1

x²+1/x² = x³+1/x³ = x⁴+1/x⁴ = 1