Question

if x^8+1/x^8=38 find x^4-1/x^4

Answer 1

${x}^{8} + \frac{1}{ {x}^{8} } = 38 \\ {( {x}^{4} )}^{2} + {( \frac{1}{ {x}^{4} }) }^{2} = 38 \\ ( { {x}^{4} - \frac{1}{ {x}^{4} } })^{2} + 2( {x}^{4} )( \frac{1}{ {x}^{4} } ) = 38 \\ {( {x}^{4} - \frac{1}{ {x}^{4} } )}^{2} = 38 - 2 \\ ( {x}^{4} - \frac{1}{ {x}^{4} } ) = \sqrt{36} \\ ( {x}^{4} - \frac{1}{ {x}^{4} } ) = 6$