Question

If 15(2x² – y²) = 7xy, find x : y; if x and y both are positive.

Answer 1

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