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Question
In the following, find the values of a and b:
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) = "a" - "b"sqrt(6)`
Solution
`(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)`
= `(7sqrt(3) - 5sqrt(2))/(4sqrt(3) + 3sqrt(2)) xx (4sqrt(3) - 3sqrt(2))/(4sqrt(3) - 3sqrt(2)`
= `(7sqrt(3)(4sqrt(3) - 3sqrt(2)) - 5sqrt(2)(4sqrt(3) - 3sqrt(2)))/((4sqrt(3))^2 - (3sqrt(2))^2`
= `(84 - 21sqrt(6) - 20sqrt(6) + 30)/(48 - 18)`
= `(110 - 41sqrt(6))/(30)`
= `(110)/(30) - (41sqrt(6))/(30)`
= `(11)/(3) - (41)/(30)sqrt(6)`
= `"a" - "b"sqrt(6)`
Hence, a = `(11)/(3)` and b = `(41)/(30)`.
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