Question

Find the values of 'a' and 'b' in each of the following: 
`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`

Answer 1

`3/[ sqrt3 - sqrt2 ] = asqrt3 - bsqrt2`

`3/[ sqrt3 - sqrt2 ] xx [ sqrt3 + sqrt2 ]/[ sqrt3 + sqrt2 ]= asqrt3 - bsqrt2`

`(3sqrt3 + 3sqrt2)/ ((sqrt3^2) - (sqrt2^2)) = asqrt3  - bsqrt2`

`(3sqrt3 + 3sqrt2) / (3-2) = asqrt3 - bsqrt2`

`(3sqrt3 + 3sqrt2)/1 = asqrt3 - bsqrt2`

`a = sqrt3 - bsqrt2 = 3sqrt3 + 3sqrt2`

∴ a= 3 and b= -3