Question

prove that 1 / 2 + root 3 + 2 / root 5 minus root 3 + 1 / 2 minus root 5 is equals to zero ​

Answer 1

The given equation is:

\frac{1}{2+\sqrt{3}}+\frac{2}{\sqrt{5}-\sqrt{3}}+\frac{1}{2-\sqrt{5}}

After rationalising the above equation, we get

=\frac{2-\sqrt{3}}{4-3}+\frac{2\sqrt{5}+2\sqrt{3}}{5-3}+\frac{2+\sqrt{5}}{4-5}

=2-\sqrt{3}+\sqrt{5}+\sqrt{3}-2-\sqrt{5}

=0

Hence proved.