Question

5 + 2 root 3 / 7 + 4 root 3 is equal to a + b root 3

Answer 1

​ By rationalization, we get
(5 + 2√3)(7 - 4√3) / (7 +4 √3) (7 - 4√3) = a + b√3
35 - 20√3 + 14√3 – 24 = a + b√3
11 - 6√3 = a + b√3
On equating the above equation, we get
a = 11 and b = -6