If ‘a’ and ‘b’ are rational numbers, find the values of a and b in the equations. √3+√2/√3-√2 = a + b√6

Question

If ‘a’ and ‘b’ are rational numbers, find the values of a and b in the equations.

\(\frac {\sqrt3+\sqrt2}{\sqrt3-\sqrt2} = a + b\sqrt6\)

√3+√2/√3-√2 = a + b√6

Answer 1

Given that \(\frac {\sqrt3+\sqrt2}{\sqrt3-\sqrt2} = a + b\sqrt6\)

Rationalising the denominator we get

Comparing 5 + 2√6 with a + b√6 

We have a = 5 and b = 2