Question

if x-1/x=4find the value of x^4+1/x^4​

Answer 1

$given \: that \\ x - \frac{1}{x} = 4 \\ squaring \: both \: sides.. \\ {(x - \frac{1}{x} )}^{2} = {4}^{2} \\ {x}^{2} - 2x( \frac{1}{x} ) + \frac{1}{ {x}^{2} } = 16 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 18 \\ again \: squaring... \\ {{( {x}^{2} } + \frac{1}{ {x}^{2} } ) }^{2} = {18}^{2} \\ {x}^{4} + 2 + \frac{1}{ {x}^{4} } = 234 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 232$

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