Question

Tính:

A= \(\frac{1}{1+\sqrt{\frac{2}{3}}+\sqrt{\frac{2}{5}}}+\frac{1}{1+\sqrt{\frac{3}{5}}+\sqrt{\frac{3}{2}}}+\frac{1}{1+\sqrt{\frac{5}{2}}+\sqrt{\frac{5}{3}}}\)

Answer 1

\(A=\frac{1}{\sqrt{2}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{5}}\right)}+\frac{1}{\sqrt{3}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{5}}\right)}+\frac{1}{\sqrt{5}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{5}}\right)}\)

\(=\frac{1}{\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{5}}\right)}\left(\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{5}}\right)\)

=1