Question

with explanation only​

Answer 1

Answer:

$x = 3 - \sqrt{8} \\ \frac{1}{x} = \frac{1}{3 - \sqrt{8} } \\ \frac{1}{x} = \frac{1}{3 - \sqrt{8} } \times \frac{3 + \sqrt{8} }{3 + \sqrt{8} } \\ \frac{1}{x} = \frac{3 + \sqrt{8} }{ {3}^{2} - { \sqrt{8} }^{2} } \\ \frac{1}{x} = 3 + \sqrt{8}$

$x = 3 - \sqrt{8} \\ {x}^{4} = {( {3 - \sqrt{8}) }^{2} )}^{2} \\ {x}^{4} = {(9 + 8 - 6 \sqrt{8} )}^{2} \\ {x}^{4} = {(17 - 6 \sqrt{8}) }^{2} \\ {x}^{4} = 284 - 204 \sqrt{8} + 288 \\ {x}^{4} = 572 - 204 \sqrt{8}$

$\frac{1}{x} = 3 + \sqrt{8} \\ \frac{1}{ {x}^{4} } = 572 + 204 \sqrt{8}$

${x}^{4} + \frac{1}{ {x}^{4} } \\ 572 - 204 \sqrt{8} + 572 + 204 \sqrt{8} \\ 1144$

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