Question

find a and b, if root 2+root 3 by 3 root 2-2 root 3=a+b root 6

Answer 1

here typing mistake , I think

question is

(√2 + √3)/( 3√2 -2√3) = a -b√6

( √2 + √3)( 3√2 + 2√3)/{ (3√2)² - (2√3)² }

(6 + 3√6 + 2√6 + 6 )/( 18 - 12)

(12 + 5√6)/6

2 +( 5/12)√6 = a - b√6

so, a = 2 and b = - 5/12

Answer 2

after rationalisation

(root2+root3)(root3+root2)/(root3-root2 )(root3+root2)

= (root3+root2)^2

= 3+2 +2root6

= 5+3root6

after comparing

a =5 and b =3