Question

Si:
x + y = 6
xy = 20

Hallar: $\frac{x}{y}$ + $\frac{y}{x}$

Answer 1

Tienes lo siguiente:
$\frac{x}{y} + \frac{y}{x}= \frac{x^2+y^2}{xy} \\ \\ (x+y)^2=6^2\\x^2+2xy+y^2=36 \\ x^2+y^2=36-2xy=36-2(20)=-4 \\ \\ \to \frac{x}{y} +\frac{y}{x}= \frac{-4}{20}\boxed{=- \frac{1}{5}}$

Saludos!