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Question
In the following, find the values of a and b:
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) = "a" - "b"sqrt(77)`
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Solution
`(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)`
= `(sqrt(11) - sqrt(7))/(sqrt(11) + sqrt(7)) xx (sqrt(11) - sqrt(7))/(sqrt(11) - sqrt(7)`
= `(sqrt(11) - sqrt(7))^2/((sqrt(11))^2 - (sqrt(7))^2`
= `((sqrt(11))^2 + (sqrt(7))^2 - 2 xx sqrt(11) xx sqrt(7))/(11 - 7)`
= `(11 + 7 - 2sqrt(77))/(4)`
= `(18 - 2sqrt(77))/(4)`
= `(18)/(4) - (2)/(4)sqrt(77)`
= `(9)/(2) - (1)/(2)sqrt(77)`
= `"a" - "b"sqrt(77)`
Hence, a = `(9)/(2)` and b = `(1)/(2)`.
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