Question

Find the values of 'a' in each of the following :

If $\frac{\sqrt{7}-2}{\sqrt{7}+2}=a\sqrt{7}+b$, then $a=-\frac{m}{3}$
where m is

Answer 1

$Werationalizethedenominator,\frac{\sqrt{7}-2}{\sqrt{7}+2}\ast \frac{\sqrt{7}-2}{\sqrt{7}-2}=\frac{4+7-4\sqrt{7}}{7-4}=\frac{11-4\sqrt{7}}{3}⟹b=11/3,a=-4/3$