Question

If x+1/x= sqrt7 then find x^4+1/x^4

Answer 1

Hello Mate!

$x + \frac{1}{x} = \sqrt{7} \\ now \: on \: squaring \: both \: sides \\ {(x + \frac{1}{x}) }^{2} = { \sqrt{7} }^{2} \\ {x}^{2} + {( \frac{1}{x}) }^{2} + 2 \times x \times \frac{1}{x} = 7 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 - 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 5 \\ now \: again \: square \: bot \: sides \\ {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {5}^{2} \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } = 25 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 25 - 2 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 23$

Hope it helps☺!✌