Question

$1-[\frac{1+\sqrt{3}}{2}-\frac{1}{\sqrt{3}+1}]$ is equal to

• A. $\sqrt{3}$
• B. $1$
• C. $2\sqrt{3}$
• D. $0$

Answer 1

The correct option is D $0$

$1-[\frac{1+\sqrt{3}}{2}-\frac{1}{\sqrt{3}+1}]$

$=1-[\frac{1+\sqrt{3}}{2}-\frac{1(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}]$

$=1-[\frac{1+\sqrt{3}}{2}-\frac{(\sqrt{3}-1)}{(\sqrt{3}{)}^2-1}]$

$=-[\frac{1+\sqrt{3}}{2}-\frac{(\sqrt{3}-1)}{2}]$

$=1-\left[\frac{1+\sqrt{3}-\sqrt{3}+1}{2}\right]$

$=1-1$

$=0$