Question

If $$x^2 + 4y^2 = 4xy$$, find $$x : y$$.

Answer 1

Rearrange the terms: $$x^2 - 4xy + 4y^2 = 0$$ 

Recognize the perfect square: $$(x - 2y)^2 = 0$$ 

Taking the square root: $$x - 2y = 0 \implies x = 2y$$ 

Find the ratio: $$\frac{x}{y} = \frac{2}{1}$$ 

Therefore, $$x : y = 2 : 1$$.