Question

x - 1/x = -2 to (x)4 + 1/(x)4 =?​

Answer 1

$x - \frac{1}{x} = - 2$

${(x - \frac{1}{x} )}^{2} = {( - 2)}^{2}$

${x}^{2} + \frac{1}{ {x}^{2} } - 2( \cancel x)( \frac{1}{ \cancel x} ) = 4$

${x}^{2} + \frac{1}{ {x}^{2} } - 2 = 4$

${x}^{2} + \frac{1}{ {x}^{2} } = 4 + 2$

${x}^{2} + \frac{1}{ {x}^{2} } = 6$

${( {x}^{2} + \frac{1}{ {x}^{2} } ) }^{2} = {(6)}^{2}$

${x}^{4} + \frac{1}{ {x}^{4} } + 2 \cancel{{(x)}^{2} } {( \frac{1}{ \cancel{{x}^{2}} }) } = 36$

${x}^{4} + \frac{1}{ {x}^{4} } = 36 - 2$

${x}^{4} + \frac{1}{ {x}^{4} } = 34$