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