Question

If 15(2x^2 - y^2) = 7xy find x:y if x and y both are positive

Answer 1

Sol :
Given 15( 2x2 - y2 ) = 7xy

⇒ 30x2 - 7xy - 15y2 = 0

⇒ 30x2 - 25xy + 18xy - 15y2 = 0

⇒ 5x(6x - 5y) + 3y(6x - 5y) = 0

5x + 3y = 0 and 6x - 5y = 0

5x = -3y and 6x = 5y

x / y = -3 / 5 and x / y = 5 / 6.

x : y = -3 :5 or 5 : 6.

Answer 2

Answer:

15(2x² - y²) = 7xy

30x²-15y² = 7xy

30x²-7xy-15y²=0

30x²-25xy+18xy-15y²=0

5x(6x-5y)+3y(6x-5y)=0

(5x+3y)(6x-5y) = 0

5x+3y = 0 or 6x-5y=0

5x = -3y   or 6x = 5y

x/y = -3/5  or 6/5 = y/x

x/y = 5/6

x:y =5:6

we will ignore x/y = -3/5 as both numbers are given positive and a negative vaue will not come in answer