Question

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

Answer 1

\(\frac{\sqrt{3}}{1-\sqrt[]{\sqrt{3}}+1}+\frac{\sqrt{3}}{1+\sqrt{\sqrt{3}}+1}\)

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

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

= \(\frac{2\sqrt{3}+\sqrt{3\sqrt{3}}}{4-\sqrt{3}}+\frac{2\sqrt{3}-\sqrt{3\sqrt{3}}}{4-\sqrt{3}}\)

= \(\frac{4\sqrt{3}}{4-\sqrt{3}}\)

Chúc bạn học tốt nhé !