সরলতম মান নির্ণয় করো :
\(\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\) \(+\cfrac{2\sqrt2}{\sqrt5+\sqrt7}\) Madhyamik 2018


\(\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\) \(+\cfrac{2\sqrt2}{\sqrt5+\sqrt7}\)
\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)+\cfrac{2√2}{√7+√5}\)
\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\)

\( +\cfrac{2√2 (√7-√5)}{(√7+√5)(√7-√5)}\)


\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\)

\(+\cfrac{2√2 (√7-√5)}{7-5}\)


\(=\sqrt7(\sqrt5–\sqrt2)−\sqrt5(\sqrt7–\sqrt2)\)

\(+\cfrac{\cancel2√2 (√7-√5)}{\cancel2}\)


\(=√35-√14-√35+√10+√14-√10\)
\(=0\)

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