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Question
In the following, find the values of a and b.
`(sqrt(3) - 1)/(sqrt(3) + 1) = "a" + "b"sqrt(3)`
Solution
`(sqrt(3) - 1)/(sqrt(3) + 1)`
= `(sqrt(3) - 1)/(sqrt(3) + 1) xx (sqrt(3) - 1)/(sqrt(3) - 1)`
= `(sqrt(3) - 1)^2/((sqrt(3))^2 - (1)^2`
= `(3 -2 xx sqrt(3) xx 1 + 1)/(3 - 1)`
= `(4 - 2sqrt(3))/(2)`
= `2 - sqrt(3)`
= `2 + (-1) sqrt(3)`
= `"a" + "b"sqrt(3)`
Hence, a = 2 and b = -1.
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