Question

please solve this question .
please solve any one of it correctly . the answer of this question are give there
please solve .​

Answer 1

Step-by-step explanation:

$x = 5 - 2 \sqrt{6} \\ \dfrac{1}{x} = \dfrac{1}{5 - 2 \sqrt{6} } \\ = \dfrac{1(5 + 2 \sqrt{6} ) }{(5 - 2 \sqrt{6})(5 + 2 \sqrt{6}) } \\ = \dfrac{5 + 2 \sqrt{6} }{( {5})^{2} - {(2 \sqrt{6}) }^{2} } \\ = \dfrac{5 + 2 \sqrt{6} }{25 - 24} \\ = \dfrac{5 + 2 \sqrt{6} }{1} \\ = 5 + 2 \sqrt{6} \\ now \\ x + \dfrac{1}{x} = 5 - 2 \sqrt{6} + 5 + 2 \sqrt{6} \\ x + \dfrac{1}{x} = 10 \\ squaring \: both \: sides \\ {(x + \dfrac{1}{x}) }^{2} = {10}^{2} \\ {x}^{2} + \dfrac{1}{ {x}^{2} } + 2x \: \dfrac{1}{x} = 100 \\ {x}^{2} + \dfrac{1}{ {x}^{2} } + 2 = 100 \\ {x}^{2} + \dfrac{1}{ {x}^{2} } = 100 - 2 \\ {x}^{2} + \dfrac{1}{ {x}^{2} } = 98$

Answer 2

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