Question

If x⁴+1/x⁴=2 find value of X+1/x

Answer 1

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$x {}^{4} + \frac{1}{x {}^{4} } = 2 \\ \\ ( x{}^{2} + \frac{1}{x {}^{2}} ) {}^{2} = ( \sqrt{2} ) {}^{2} \\ \\ x {}^{2} + \frac{1}{x { }^{2} } + 2 = 2 \\ \\ x {}^{2} + \frac{1}{x { }^{2} } = 2 - 2 \\ \\ (x + \frac{1}{x} ) {}^{2} = 0 \\ \\ x + \frac{1}{x} = 0$


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