Question

find the values of a and b , if root 2 + root 3/3 root 2 - 2 root 3 = a +b root 16

Answer 1

LHS =(√2+√3)/3√2-2√3

=(√2+√3)(3√2+2√3)/18-12

=(3*2+2√6+3√6+2*3)/6

=(6+5√6+6)/6

(12+5√6)/6

comparing with RHS

we have

a=12/6=2

b=5/6

but in the question it may be a+b√6