Question

The value of a if $\frac{5+\sqrt{3}}{7-4\sqrt{3}}=a+\sqrt{3}b$ is

Answer 1

Given $\frac{5+\sqrt{3}}{7-4\sqrt{3}}=a+\sqrt{3}b$

$⟹a+\sqrt{3}b=\frac{(5+\sqrt{3})(7+4\sqrt{3})}{(7-4\sqrt{3})(7+4\sqrt{3})}=\frac{35+7\sqrt{3}+20\sqrt{3}+12}{49-48}=47+27\sqrt{3}$

$⟹a=47,b=27$