Question

If x+1/x=4,find x4 +1/x4

Answer 1

$x + \frac{1}{x} = 4 \\ \\ squaring \: both \: he \: sides \\ \\ (x + \frac{1}{x}) {}^{2} = (4) {}^{2} \\ \\ (x {}^{2} + \frac{1}{x {}^{2} } + 2) = 16 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 14 \\ \\ \\ now \: again \: we \: find \: te \: squaring \\ \\ (x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} = (14) {}^{2} \\ x {}^{4} + \frac{1}{x {}^{4} } + 2 = 196 \\ \\ x {}^{4} + \frac{1}{x {}^{4} } = 194$
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