Question

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

Answer 1

Divide through by $y^2$

$(\frac{x}{y}{)}^2+6=5(\frac{x}{y})$

Let $\frac{x}{y}=z$

$z^2-5z+6=0$

$(z-2)(z-3)=0$

$\Rightarrow z=2or3$

$ie,\frac{x}{y}=2or3$