Question

\(\left(\sqrt{2}+\sqrt{2+\sqrt{3}}\right)\left(\sqrt{2}-\sqrt{2-\sqrt{3}}\right)\)

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Mọi người giúp e với ạ. Em cảm ơn ạ.

Answer 1

\(=\frac{1}{2}\left(2+\sqrt{4+2\sqrt{3}}\right)\left(2-\sqrt{4-2\sqrt{3}}\right)\)

\(=\frac{1}{2}\left(2+\sqrt{\left(\sqrt{3}+1\right)^2}\right)\left(2-\sqrt{\left(\sqrt{3}-1\right)^2}\right)\)

\(=\frac{1}{2}\left(2+\sqrt{3}+1\right)\left(2-\sqrt{3}+1\right)\)

\(=\frac{1}{2}\left(3+\sqrt{3}\right)\left(3-\sqrt{3}\right)=3\)