mathematics

Question

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458

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

$\frac{x}{y}+\frac{y}{x}=\frac{25}{12},$

$x^2-y^2=7$

Straight Oct 13, 2021

Melody · Answer 1 · 2021-10-14T09:13:55

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.

Straight · Answer 2 · 2021-10-15T04:58:43

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