Question

Find the value of a $a$ and $b$ respectively, if $\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}=a+b\sqrt{7}$.

• A. $0,\frac{-2}{3}$
• B. $1,-1$
• C. $\frac{2}{3},0$
• D. $1,\frac{-2}{3}$

Answer 1

The correct option is A $0,\frac{-2}{3}$

Solving L.H.S

$=\frac{\sqrt{7}-1}{\sqrt{7}+1}-\frac{\sqrt{7}+1}{\sqrt{7}-1}$

$=\frac{(\sqrt{7}-1)\times (\sqrt{7}-1)-(\sqrt{7}+1)\times (\sqrt{7}+1)}{(\sqrt{7}+1)(\sqrt{7}-1)}$

$=\frac{-4\sqrt{7}}{(\sqrt{7}{)}^2-1}$

$=\frac{-4\sqrt{7}}{6}$

$=\frac{-2}{3}\sqrt{7}$

Now, by comparing it to R.H.S

we get,

$a=0$ and $b=\frac{-2}{3}$.