Question

X = 3+√8 find xsquare + 1/xsquare and x4 +1/xfour​

Answer 1

X = 3+√8

$\frac{1}{x} = \frac{1}{3 + \sqrt{8} } = \frac{1}{3 + \sqrt{8} } \times \frac{3 - \sqrt{8} }{3 - \sqrt{8} } = ( {3 - \sqrt{8} })$

Now,

${x}^{2} + \frac{1}{ {x}^{2} } = {(3 + \sqrt{8}) }^{2} + {(3 - \sqrt{8} )}^{2} \\ = 9 + 8 + 6 \sqrt{8} + 9 + 8 - 6 \sqrt{8} \\ = 34$

Now,

${( {x}^{2} + { \frac{1}{ {x}^{2} } }) }^{2} = {(34)}^{2} \\ = > {x}^{4} + { \frac{1}{ {x}^{4} } } + 2. {x}^{2} . \frac{1}{ {x}^{2} } =1156 \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 1156 - 2 \\ = > {x}^{4} + \frac{1}{ {x}^{4} } = 1154$