# If a=5+2âˆš6 and b=1/a, then what will be the value of a^2+b^2

$\begin{array}{l} As \ \ \ a=5+2 \sqrt{6} \\ \\ and \ b=\frac{1}{a}=\frac{1}{5+2 \sqrt{6} }=\frac{5-2 \sqrt{6} }{(5+2 \sqrt{6} )*(5-2 \sqrt{6} )}=5-2 \sqrt{6} \\ \\ \text { Also, } \quad a^{2}+b^{2}=(a+b)^2-2 a b \\ \text { Here. } \quad a+b=(5+2 \sqrt{6})+(5-2 \sqrt{6})=10 \\ \qquad \begin{array}{l} a b=(5+2 \sqrt{6})(5-2 \sqrt{6})=5^{2}-(2 \sqrt{6})^{2}=25-24=1 \\ a^{2}+b^{2}=10^{2}-2 \times 1=100-2=98 \end{array} \end{array}$

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