Determine all pairs (\(x,y\)) of real numbers that satisfy the system of equations

\(\frac{x}{y}+\frac{y}{x}=\frac{25}{12}, \)

\(x^2-y^2=7\)

Straight Oct 13, 2021

#1**+1 **

Solve the 2 equations simultaneously and you get (3,4) and (-3,-4)

You have \(x^2+y^2=\frac{25}{12}xy\qquad and \qquad x^2=7-y^2\)

The algebra is messy and the numbers are big but it is very doable.

Here is the graphical soln.

https://www.geogebra.org/classic/sbdg4fsw

Melody Oct 14, 2021