Find the ratio of X to Y in the following: x^2+y^2 = (x+2y) ^2

-3 : 4

Step-by-step explanation:

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

x² + y² = x² + 4xy + 4y²

3y² + 4xy = 0

y (3y + 4x) = 0

3y + 4x = 0

3y = - 4x

x/y = - 3/4

x : y

-3 : 4

-3/4

Step-by-step explanation:

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

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

Foil the right side

x^2 + y^2 = x^2 + 2xy + 2xy + 4y^2

Combine like terms

x^2 + y^2 = x^2 + 4xy + 4y^2

Subtract x^2 + y^2 from each side

x^2 + y^2 - x^2 - y^2 = x^2 + 4xy + 4y^2 - x^2 - y^2

0 = 4xy + 3y^2

Subtract 3y^2 to each side

-3y^2 = 4xy

Divide each side by y^2

-3y^2 / y^2 = 4xy / y^2

-3 = 4x/y

Divide each side by 4

-3/4 = x/y

The ratio is - 3/4