Question

Thuc hien phep tinh: B=\(\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{2}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

Answer 1

bạn coi kĩ lại đề đi bạn

Answer 2

\(B=\dfrac{2+\sqrt{3}}{\sqrt{2}+\sqrt{2+\sqrt{3}}}+\dfrac{2-\sqrt{3}}{\sqrt{2}-\sqrt{2-\sqrt{3}}}\)

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

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

\(=\sqrt{2}\cdot\dfrac{6-2\sqrt{3}+3\sqrt{3}-3+6+2\sqrt{3}-3\sqrt{3}-3}{6}\)

\(=\dfrac{1}{3\sqrt{2}}\cdot\dfrac{6}{1}=\sqrt{2}\)