Question

If x+1/x=6 find the value of x*4+1/×*4

Answer 1

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$x + \frac{1}{x} = 6 \\ \\ \bf on \: squaring \: both \: sides : \\ \\ (x + \frac{1}{x} ) {}^{2} = (6) {}^{2} \\ \\ x {}^{2} + \frac{1}{x {}^{2} } + 2 = 36 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 36 - 2 \\ \\ x {}^{2} + \frac{1}{x {}^{2} } = 34$

Now,

$\bf Again \: squaring \: both \: sides : \\ \\ (x {}^{2} + \frac{1}{x {}^{2} } ) {}^{2} = (34) {}^{2} \\ \\ x {}^{4} + \frac{1}{x {}^{4} } + 2 = 1156 \\ \\ x {}^{4} + \frac{1}{x {}^{4} } = 1156 - 2 \\ \\ \boxed { \boxed{ \red{ \bold{x {}^{4} + \frac{1}{x {}^{4} } = 1154}}}}$

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