Question

If x+1÷x=√7 then what is the value of x4-1÷x4=?

Answer 1

$x + \frac{1}{x} = \sqrt{7} \\ \\ Squaring \: \: both \: \: sides \: , \\ {x}^{2} + \frac{1}{ {x}^{2} } + 2(x)( \frac{1}{x} ) = 7 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 5 \\ \\ Squaring \: \: both \: \: sides \: \: again \: , \\ \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2( {x}^{2})( \frac{1}{ {x}^{2} } ) = 25 \\ \\ \large \: \boxed{ {x}^{4} + \frac{1}{ {x}^{4} } = 23}$