Question

Si x²+y²= 6xy
x≠y
Hallar cuanto vale la siguiente operación
x+y/x-y=?

Answer 1

$z= \dfrac{x+y}{x-y}\\ \\ \\ z^2=\dfrac{(x+y)^2}{(x-y)^2}\\ \\ \\ z^2= \dfrac{x^2+y^2+2xy}{x^2+y^2-2xy}\\ \\ \\ z^2= \dfrac{6xy+2xy}{6xy-2xy}\\ \\ \\ z^2=\dfrac{8xy}{4xy}\\ \\ \\ z^2=2\\ \\ z=\pm\sqrt{2}\\ \\ \\ \boxed{\dfrac{x+y}{x-y}=\pm\sqrt{2}}$