Question

Find the value of a and b if 5+2√3/7+4√3 = a+√3b

Answer 1

5+2 root 3 / 7+ 4 root 3
 on rationalising 
(5+ root 3/ 7+4 root 3 ) x (7-4 root 3/ 7 - root 3)
{(5+2root 3)(7-4 root 3)}\(7sq - 4root 3 sq)
(35 - 20root 3 + 14root 3 - 8root 3)\(49-48)
==> 35- 14 root 3 
on comparing
a = 35
b root 3 = -14 root 3
therefore b= -14

Answer 2

7√3/7+4√3=a+√3b
=
$7 \sqrt{3 \div 7 + 4 \sqrt{3 = a + \sqrt{3b} } }$