Question

Solve 25 and don't give link
Q.25. If $a=\frac{2+\sqrt{3}}{\sqrt{3}+1}andb=\frac{2-\sqrt{3}}{\sqrt{3}-1}.$ Then what is the value of a + b.

Answer 1

$$\begin{gathered} Hi, \\ a+b=\frac{2+\sqrt{3}}{\sqrt{3}+1}+\frac{2-\sqrt{3}}{\sqrt{3}-1} \\ =\frac{2\sqrt{3}-2+3-\sqrt{3}+2\sqrt{3}+2-3-\sqrt{3}}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)} \\ =\frac{2\sqrt{3}}{\left(\sqrt{3}+1\right)\left(\sqrt{3}-1\right)} \\ =\frac{2\sqrt{3}}{\left({\left(\sqrt{3}\right)}^2-1^2\right)}=\frac{2\sqrt{3}}{3-1}=\sqrt{3} \end{gathered}$$