Let S=left{ x : x in R text { and }(sqrt{3}+s | vedclass

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Question

Let $(\sqrt{3}+\sqrt{2})^{ x ^2-4}= t$

$t +\frac{1}{ t }=10$

$\Rightarrow \quad t =5+2 \sqrt{6}, 5-2 \sqrt{6}$

$\Rightarrow \quad (\sqrt{3}+\

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Vedclass · Answer

Let $(\sqrt{3}+\sqrt{2})^{ x ^2-4}= t$

$t +\frac{1}{ t }=10$

$\Rightarrow \quad t =5+2 \sqrt{6}, 5-2 \sqrt{6}$

$\Rightarrow \quad (\sqrt{3}+\sqrt{2})^{ x ^2-4}=5+2 \sqrt{6}, 5-2 \sqrt{6}$

$\Rightarrow \quad x ^2-4=2,-2 \quad 	ext { or } x ^2=6,2$

$\Rightarrow \quad x =\pm \sqrt{2}, \pm \sqrt{6}$

Let $S=\left\{ x : x \in R \text { and }(\sqrt{3}+\sqrt{2})^{ x ^2-4}+(\sqrt{3}-\sqrt{2})^{ x ^2-4}=10\right\} \text {. }$ Then $n ( S )$ is equal to

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