Question

Rút gọn

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

Answer 1

Ta có: B=\(\frac{\sqrt{2+\sqrt{3}}}{\sqrt{2-\sqrt{3}}}-\frac{\sqrt{2-\sqrt{3}}}{\sqrt{2+\sqrt{3}}}=\frac{2+\sqrt{3}-2+\sqrt{3}}{\sqrt{\left(2-\sqrt{3}\right)\left(2+\sqrt{3}\right)}}=\frac{2\sqrt{3}}{\sqrt{4-\sqrt{3}^2}}=\frac{2\sqrt{3}}{1}=2\sqrt{3}\)