Question

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

Answer 1

(5 + 2√3) / (7 +4 √3) = a + b√3

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