Question

$\frac{\sqrt{5}-2}{\sqrt{5}+2}-\frac{\sqrt{5}+2}{\sqrt{5}-2}=$

• A. $8\sqrt{5}$
• B. $-8\sqrt{5}$
• C. $6\sqrt{5}$
• D. $-6\sqrt{5}$

Answer 1

The correct option is

B

$-8\sqrt{5}$

$\frac{\sqrt{5}-2}{\sqrt{5}+2}-\frac{\sqrt{5}+2}{\sqrt{5}-2}$

$=\frac{(\sqrt{5}-2{)}^2-(\sqrt{5}+2{)}^2}{(\sqrt{5}{)}^2-(2{)}^2}$ [Since, $(a-b{)}^2-(a+b{)}^2=-4ab$]

$=\frac{-(4\cdot \sqrt{5}\cdot 2)}{1}$

$=-8\sqrt{5}$.