Question

Find $\frac{x}{y}$, when $x^2+6y^2=5xy$.

Answer 1

$x^2-5xy+6y^2=0$

$\Rightarrow x^2-3xy-2xy+6y^2=0$

$\Rightarrow x(x-3y)-2y(x-3y)=0$

$\Rightarrow (x-2y)(x-3y)=0$

Therefore, $x=3y.$ $\frac{x}{y}=3.$ Or. $x=2y,\frac{x}{y}=2$.