Question

if x-1/x=7 find value of x to the power 4 +1/x to the power 4

Answer 1

The answer is given below :

$Now, \: \: x - \frac{1}{x} = 7 \\ \\ Squaring \: \: both \: \: sides \: \: we \: \: get, \\ \\ {(x - \frac{1}{x}) }^{2} = {7}^{2} \\ \\ or \: \: {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} = 49 \\ \\ or \: \: {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 49 \\ \\ so \: \: {x}^{2} + \frac{1}{ {x}^{2} } = 51$

Hence,

${x}^{4} + \frac{1}{ {x}^{4} } \\ \\ = {( {x}^{2} + \frac{1}{ {x}^{2} } )}^{2} - 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } \\ \\ = {51}^{2} - 2 \\ \\ = 2601 - 2 \\ \\ = 2599$

Thank you for your question.