Question

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Answer 1

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Answer 2

$x = 5 - 2 \sqrt{6} \\ \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6} } \times \frac{5 + 2 \sqrt{6}}{ 5 + 2 \sqrt{6} } = \frac{ 5 + 2 \sqrt{6} }{25 - 24} = 5 + 2 \sqrt{6} \\ x + \frac{1}{x} = 5 - 2 \sqrt{6} + 5 + 2 \sqrt{6} \\ x + \frac{1}{x} \: = 10 \\ squring \: on \: both \: sides \\ (x + \frac{1}{x}) ^{2} \: = 10 ^{2} \\ x ^{2} + \frac{1}{x ^{2} } + 2 = 100 \\ x ^{2} + \frac{1}{x ^{2} } = 100 - 2 \\ x ^{2} + \frac{1}{x ^{2} } = 98$