\(x=\sqrt3+\sqrt2\),\(y=\cfrac{1}{\sqrt3+\sqrt2}\) হলে \((x+y)^2+(x-y)^2\) এর মান নির্ণয় করো । Madhyamik 2009
\(y=\cfrac{1}{\sqrt3+\sqrt2}\)
\(=\cfrac{(\sqrt3-\sqrt2)}{(\sqrt3+\sqrt2)(\sqrt3-\sqrt2)}\)
\(=\cfrac{(\sqrt3-\sqrt2)}{3-2}\)
\(=\sqrt3-\sqrt2\)
\(\therefore (x+y)=\sqrt3+\sqrt2+\sqrt3-\sqrt2=2\sqrt3\)
এবং, \((x-y)=\sqrt3+\sqrt2-\sqrt3+\sqrt2=2\sqrt2\)
\(\therefore (x+y)^2+(x-y)^2=(2\sqrt3)^2+(2\sqrt2)^2\)
\(=12-8=4\) (Answer)