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Question
In the following, find the values of a and b:
`(sqrt(3) - 2)/(sqrt(3) + 2) = "a"sqrt(3) + "b"`
Solution
`(sqrt(3) - 2)/(sqrt(3) + 2)`
= `(sqrt(3) - 2)/(sqrt(3) + 2) xx (sqrt(3) - 2)/(sqrt(3 - 2)`
= `(sqrt(3)(sqrt(3) - 2) - 2(sqrt(3) - 2))/((sqrt(3))^2 - (sqrt(2))^2`
= `(3 - 2sqrt(3) - 2sqrt(3) + 4)/(3 - 4)`
= `(7 - 4sqrt(3))/(-1)`
= `-(7 - 4sqrt(3))`
= `-7 + 4sqrt(3)`
= `4sqrt(3) - 7`
= `4sqrt(3) + (-7)`
= `"a"sqrt(3) + "b"`
Hence, a = 4 and b = -7.
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