Question

Find the values of 'a' and 'b' in each of the following:
`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

Answer 1

`[5 + 3sqrt2]/[ 5 - 3sqrt2] = a + bsqrt2`

`[5 + 3sqrt2]/[ 5 - 3sqrt2] xx [5 + 3sqrt2]/[ 5 + 3sqrt2]= a + bsqrt2`

`[ ( 5 + 3sqrt2)^2 ]/[ (5)^2 - ( 3sqrt2)^2 ] = a + bsqrt2`

`[ 25 + 18 + 30sqrt2 ]/[ 25 - 18 ] = a + bsqrt2`

`[ 43 + 30sqrt2 ]/7 = a + bsqrt2`

`a = 43/7,  b = 30/7`