Question

Please answer me fast ​

Answer 1

Answer:

${x}^{2} + \frac{1}{ {x}^{2} } = 83 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 6887$

Step-by-step explanation:

$x - \frac{1}{x} = 9 \\ squaring \: on \: both \: the \: sides \\ {(x - \frac{1}{x}) }^{2} = {(9)}^{2} \\ {(x)}^{2} + { (\frac{1}{x}) }^{2} - 2(x)( \frac{1}{x} ) = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 81 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 81 + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 83 \\ squaring \: on \: both \: the \: sides \\ {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {(83)}^{2} \\ {( {x}^{2} )}^{2} + { (\frac{1}{ {x}^{2} }) }^{2} + 2( {x}^{2} )( \frac{1}{ {x}^{2} } ) = 6889 \\ {x}^{4} + \frac{1}{ {x}^{4} } + 2 = 6889 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 6889 - 2 \\ {x}^{4} + \frac{1}{ {x}^{4} } = 6887$