If y^2-x^2=5(y-x)^2 find x:y

x:y = 1:1 or 2:3

Step-by-step explanation:

By a difference of squares, we get:

(y+x)(y-x)=5(y-x)^2

move all to one side:

(y+x)(y-x) - 5(y-x)^2 = 0

take a common factor of (y - x) out and expand and simply the other factor:

(y - x)[y+x-5(y-x)] = 0

(y - x)(-4y + 6x) = 0

By the null factor rule:

x = y

=> x:y = 1:1

or

6x = 4y

=>

x:y = 4:6

x:y = 2:3

2

3,000,540

step-by-step explanation: