If a=5+2 sqrt{6} and b=frac{1}{a}, then what | vedclass

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Question

$a=5+2 \sqrt{6}$

$b=\frac{1}{a}=\frac{1}{5+2 \sqrt{6}}=\frac{1}{5+2 \sqrt{6}} 	imes \frac{5-2 \sqrt{6}}{5-2 \sqrt{6}}=\frac{5-2 \sqrt{6}}{5^{2}-(2

Vedclass · Accepted Answer

$98$

Vedclass · Answer

$a=5+2 \sqrt{6}$

$b=\frac{1}{a}=\frac{1}{5+2 \sqrt{6}}=\frac{1}{5+2 \sqrt{6}} 	imes \frac{5-2 \sqrt{6}}{5-2 \sqrt{6}}=\frac{5-2 \sqrt{6}}{5^{2}-(2 \sqrt{6})^{2}}=\frac{5-2 \sqrt{6}}{25-24}=5-2 \sqrt{6}$

Therefore, $\quad a^{2}+b^{2}=(a+b)^{2}-2 a b$

Here, $\quad a+b=(5+2 \sqrt{6})+(5-2 \sqrt{6})=10$

$\quad a b=(5+2 \sqrt{6})(5-2 \sqrt{6})=5^{2}-(2 \sqrt{6})^{2}=25-24=1$

Therefore, $\quad a^{2}+b^{2}=10^{2}-2 	imes 1=100-2=98$

If $a=5+2 \sqrt{6}$ and $b=\frac{1}{a},$ then what will be the value of $a^{2}+b^{2} ?$

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