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# mathematics

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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
+117466
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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
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You are right, so it stands on the book too!

Oct 15, 2021