Question

$\Large\mathfrak \purple {\bigstar ~~Question:- }$



Find rational numbers 'a' and 'b' so that - $\bf \dfrac{5 \: + \: 2 \sqrt{3}}{7 \: + \: 4 \sqrt{3}} = \: a \: + \: b \: \sqrt{3}$

Note !

Irrelevant answers will be reported...​

Answer 1

First multiply this by 7 - 4 root 3 u’ll get 49-48 in the denominator=> 1 in the denominator. The numerator u’ll get 5+2 root 3 x 7-4 root 3 => 35 - 20 root 3 + 14 root 3- 24=> 11 - 6 root 3
Therefore ans: a=11 and b=-6