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Question
Find the values of 'a' and 'b' in each of the following :
`[2 + sqrt3]/[ 2 - sqrt3 ] = a + bsqrt3`
Solution
`[ 2 + sqrt3 ]/[ 2 - sqrt3 ] xx [ 2 + sqrt3 ]/[ 2 + sqrt3] = a + bsqrt3`
= `[ (2 + sqrt3)^2 ]/[ (2)^2 - (sqrt3)^2 ] = a + bsqrt3`
= `[ 4 + 3 + 4sqrt3]/[ 4 - 3 ] = a + bsqrt3`
7 + 4√3 = a + b√3
a = 7, b = 4
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