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Question
In the following, find the values of a and b:
`(1)/(sqrt(5) - sqrt(3)) = "a"sqrt(5) - "b"sqrt(3)`
Solution
`(1)/(sqrt(5) - sqrt(3)`
= `(1)/(sqrt(5) - sqrt(3)) xx (sqrt(5) + sqrt(3))/(sqrt(5) + sqrt(3)`
= `(sqrt(5) + sqrt(3))/((sqrt(5))^2 - (sqrt(3))^2`
= `(sqrt(5) + sqrt(3))/(5 - 3)`
= `(sqrt(5) + sqrt(3))/(2)`
= `(1)/(2)sqrt(5) + (1)/(2)sqrt(3)`
= `(1)/(2)sqrt(5) - (-1/2)sqrt(3)`
= `"a"sqrt(5) - "b"sqrt(3)`
Hence, a = `(1)/(2)` and b = `-(1)/(2)`.
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