Question

If x+1/ x=9 evaluate x⁴+1/x⁴

Answer 1

$x + \frac{1}{x} = 9 \\ squaring \: on \: both \: sides \\ {(x + \frac{1}{x}) }^{2} = {(9)}^{2} \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 79$

Now,

SQUARING ON BOTH SIDES

${( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {(79)}^{2} \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2( {x}^{2} )( \frac{1}{ {x}^{2} } ) = 6241 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 6241 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 6239$