Find the value of a and b in each of the following
`(i)(3+sqrt(2))/(3-sqrt(2))=a+bsqrt(2)" "(ii)(sqrt(2)+1)/(sqrt(2)-1)=a-bsqrt(2)" "(iii)(5+4sqrt(3))/(5-4sqrt(3))=a-bsqrt(3)`

Explanation

We have
`(3+sqrt(2))/(3-sqrt(2)) = ((3+sqrt(2)))/((3-sqrt(2))) xx ((3+sqrt(2)))/((3+sqrt(2)))=((3+sqrt(2))^(2))/((3)^(2)-(sqrt(2))^(2))`
`=(3^(2) + (sqrt(2))^(2) + 2xx 3xx sqrt(2))/(9-2) = (9+2+6sqrt(2))/(7) = (11+6sqrt(2))/(7)`.
`therefore (3+sqrt(2))/(3-sqrt(2)) = a+ bsqrt(2) hArr (11)/(7) + (6)/(7)sqrt(2) = a+ b sqrt(2)`
`hArr a=(11)/(7) and b = (6)/(7).`