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Question
In the following, find the values of a and b:
`(3 + sqrt(7))/(3 - sqrt(7)) = "a" + "b"sqrt(7)`
Solution
`(3 + sqrt(7))/(3 - sqrt(7)`
= `(3 + sqrt(7))/(3 - sqrt(7)) xx (3 + sqrt(7))/(3 + sqrt(7)`
= `(3 + sqrt(7))^2/((3)^2 - (sqrt(7))^2`
= `(9 + 6sqrt(7) + 7)/(9 - 7)`
= `(16 + 6sqrt(7))/(2)`
= `8 + 3sqrt(7)`
= `"a" + "b"sqrt(7)`
Hence, a = 8 and b = 3.
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