Share

# If 15(2x2 – Y2) = 7xy, Find X: Y; If X and Y Both Are Positive. - Mathematics

Course

#### Question

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

#### Solution

15(2x^2 - y^2) = 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 = 715

30a^2 - 15 = 7a

30a^2 - 7a - 15 = 0

30a^2 - 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

Is there an error in this question or solution?