Question

Rút gọn biểu thức: C=\(\frac{1}{2+\sqrt{3}}+\sqrt{\frac{2}{6}}-\frac{2}{3+\sqrt{3}}\)

Answer 1

Lời giải:

\(C=\frac{1}{2+\sqrt{3}}+\sqrt{\frac{2}{6}}-\frac{2}{3+\sqrt{3}}=\frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}+\frac{\sqrt{3}}{3}-\frac{2(3-\sqrt{3})}{(3+\sqrt{3})(3-\sqrt{3})}\)

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

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

Answer 2

Lời giải:

\(C=\frac{1}{2+\sqrt{3}}+\sqrt{\frac{2}{6}}-\frac{2}{3+\sqrt{3}}=\frac{2-\sqrt{3}}{(2+\sqrt{3})(2-\sqrt{3})}+\frac{\sqrt{3}}{3}-\frac{2(3-\sqrt{3})}{(3+\sqrt{3})(3-\sqrt{3})}\)

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

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