Question

If x + 1/x = 9 , find x⁴ + 1/x⁴



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Answer 1

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Given,

$x + \frac{1}{x} = 9 \\ now \\ {x}^{4} + \frac{1}{ {x}^{4} } \\ = { {(x}^{2} )}^{2} + ({ { \frac{1}{ {x}^{2} } })^{2} } \\ = {( {x }^{2} + \frac{1 }{ {x}^{2} } )}^{2} - 2 \times \cancel {x}^{2} \times \frac{1}{ \cancel {x}^{2} } \\ = \{ { {(x + \frac{1}{x}) }^{2} - 2 \times x \times \frac{1}{x} } \}^{2} - 2 \\ = \{ {9}^{2} - 2 \}^{2} - 2 \\ = {(81 - 2})^{2} - 2 \\ = {79}^{2} - 2 \\ = 6239$