Question

Find the value of $a$ and $b$ if $\frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b$

Answer 1

$\frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b$....(1)

By rationalising L.H.S,

$\frac{\sqrt{7}-2}{\sqrt{7}+2}\times \frac{\sqrt{7}-2}{\sqrt{7}-2}=\frac{(\sqrt{7}-2{)}^2}{{\sqrt{7}}^2-2^2}$

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

$=\frac{11-4\sqrt{2}}{3}$....(2)

Compairing (1) and(2):

$a=\frac{-4}{3}$ and $b=\frac{11}{3}$