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Question
If 15(2x2 – y2) = 7xy, find x : y; if x and y both are positive.
Solution
15(2x2 – y2) = 7xy
`(2x^2 - y^2)/(xy) = 7/15`
`(2x)/y - y/x = 7/15`
Let `x/y = a`
`∴ 2a - 1/a = 7/15`
`(2a^2 - 1)/a = 7/15`
30a2 – 15 = 7a
30a2 – 7a – 15 = 0
30a2 – 25a + 18a – 15 = 0
5a(6a – 5) + 3(6a – 5) = 0
(6a – 5)(5a + 3) = 0
`a = 5/6, -3/5`
But a cannot be negative
∴ `a = 5/6`
`=> x/y = 5/6`
`=>` x : y = 5 : 6
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