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Question
If `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) = "p" + "q"sqrt(30)`, find the values of p and q.
Solution
`(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)`
= `(sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) + sqrt(0.75)) xx (sqrt(2.5) - sqrt(0.75))/(sqrt(2.5) - sqrt(0.75))`
= `(sqrt(2.5) - sqrt(0.75))^2/((sqrt(2.5))^2 - (sqrt(0.75))^2`
= `(2.5 - 2 xx sqrt(2.5) xx sqrt(0.75) + 0.75)/(2.5 - 0.75)`
= `(3.25 - 2 xx sqrt(0.25 xx 10) xx sqrt(0.25 xx 3))/(1.75)`
= `(3.25 - 2 xx 0.25sqrt(30))/(1.75)`
= `(3.25 - 0.5sqrt(30))/(1.75)`
= `(3.25)/(1.75) - (0.5)/(1.75)sqrt(30)`
= `(325)/(175) - (50)/(175)sqrt(30)`
= `(13)/(7) - (2)/(7)sqrt(30)`
= `(13)/(7) + (-2/7)sqrt(30)`
= p + q`sqrt(30)`
Hence, p = `(13)/(7)` and q = `-(2)/(7)`.
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