Question

If $a=\frac{1}{2-\sqrt{3}}$, $b=\frac{1}{2+\sqrt{3}}$ find the value of${\left(\frac{a+b}{a-b}\right)}^2$

• A. 3/4
• B. 2/3
• C. 4/3
• D. 4/5

Answer 1

Answer: (C)

4/3

$a=\frac{1}{2-\sqrt{3}}\times \frac{2+\sqrt{3}}{2+\sqrt{3}}=2+\sqrt{3}$
$b=2-\sqrt{3}$
$\Rightarrow a+b=4$ and $a-b=2\sqrt{3}$
$\therefore {\left(\frac{a+b}{a-b}\right)}^2={\left(\frac{4}{2\sqrt{3.}}\right)}^2=\frac{4}{3}$