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

 

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

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

 
 Oct 13, 2021
 #1
avatar+114812 
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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

 

 
 Oct 14, 2021
 #2
avatar+132 
+1

You are right, so it stands on the book too!

 
 Oct 15, 2021

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