Question

If x=5-2 root 6 find the value of x square +1/x square

Answer 1

$\huge\underline\mathcal{Answer:-}$

$x = 5 - 2 \sqrt{6} \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \\ = \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6} }{5 + 2 \sqrt{6} } \\ = \frac{5 + 2 \sqrt{6} }{25 - 24} \\ = 5 + 2 \sqrt{6} \\ {x}^{2} = {(5 - 2 \sqrt{6)} }^{2} \\ = 25 + 24 - 20 \sqrt{6} \\ = 49 - 20 \sqrt{6} \\ { (\frac{1}{x}) }^{2} = {(5 + 2 \sqrt{6}) }^{2} \\ = 25 + 24 + 20 \sqrt{6} \\ = 49 + 20 \sqrt{6} \\ {x}^{2} + {( \frac{1}{x}) }^{2} = 49 - 20 \sqrt{6} + 49 - 20 \sqrt{6} \\ = 98$

$\huge\underline\mathfrak{Answer=98}$