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Class-9»Maths

if x = 5-2root6, find the value of x²+1/x²

$x = 5 - 2 \sqrt{6} \Rightarrow \frac{1}{x} = \frac{1}{5 - 2 \sqrt{6}} = \frac{5 + 2 \sqrt{6}}{(5 - 2 \sqrt{6}) (5 + 2 \sqrt{6})} = \frac{5 + 2 \sqrt{6}}{25 - 24} = 5 + 2 \sqrt{6} \Rightarrow x + \frac{1}{x} = 5 - 2 \sqrt{6} + 5 + 2 \sqrt{6} = 10 \Rightarrow {(x + \frac{1}{x})}^{2} = 10^{2} \Rightarrow x^{2} + \frac{1}{x^{2}} + 2 = 100 \Rightarrow x^{2} + \frac{1}{x^{2}} = 100 - 2 = 98$

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