Question

pls solve the question its very tough
the correct answer with explanation will be marked as brainliest ​

Answer 1

$<marquee behavior="scroll" direction="up" scrollamount="1">SubhamSinha</marquee> <marquee behavior="scroll" direction="right" scrollamount="12">SubhamSinha</marquee> <marquee behavior="scroll" direction="left" scrollamount="20">SubhamSinha</marquee> <marquee behavior="scroll" direction="right" scrollamount="50">SubhamSinha</marquee >$

Answer 2

$\small\colorbox{lightyellow} {\text{ \bf♕ Brainliest answer }}$

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$\mathbb\red{ \tiny A \scriptsize \: N \small \:S \large \: W \Large \:E \huge \: R}$

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$\[ \begin{array}{l} \\ \displaystyle\rm \text { Sol: } \frac{-2(\sqrt{2}+\sqrt{6})}{3 \sqrt{2+\sqrt{6}}}+\sqrt{2+\sqrt{3}}+\sqrt{2+\sqrt{3}} \\\\ \displaystyle\rm \implies \frac{2 \sqrt{2}+\sqrt{6}}{3 \sqrt{2+\sqrt{3}}} \times \frac{\sqrt{2-\sqrt{3}}}{\sqrt{2 \sqrt{3}}}+\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}} \\\\ \displaystyle\rm\implies \frac{2(\sqrt{2}+\sqrt{6})(\sqrt{2-\sqrt{3}})}{3}+\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}} \\\\ \displaystyle\rm \implies\frac{2 \sqrt{2}(1+\sqrt{3})(\sqrt{2}-\sqrt{3})}{3}+\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}} \\ \\ \displaystyle\rm\implies\frac{2 \sqrt{2}(1+\sqrt{3})(\sqrt{3}-1)}{\sqrt{2} \times 3}+\sqrt{2+\sqrt{3}}+\sqrt{2-\sqrt{3}} \\\\ \displaystyle\rm \implies\frac{2}{3}(2)+\frac{(\sqrt{3}+1)}{\sqrt{2}}+\frac{(\sqrt{3}-1)}{\sqrt{2}} \\\\\implies \displaystyle\rm \frac{4}{3}+\frac{\sqrt{3}+1+\sqrt{3}-1}{\sqrt{2}} \\\\ \displaystyle\rm\implies \frac{4}{3}+\frac{2 \sqrt{3}}{\sqrt{2}} \\ \\ \displaystyle\rm\implies\frac{4}{3}+\frac{\sqrt{2} \sqrt{3}+\sqrt{6}}{\sqrt{2}} \\\\ \color{olive}\boxed{ \displaystyle\rm\implies \frac{4+3 \sqrt{6}}{3}} \end{array} \]$