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Let \(a, b, c, x, y\)  and \(z\) be real numbers such that  \(a+x \neq 0, b+y \neq 0, c+z \neq 0,\) and

\(a^2=by+cz\)

\(b^2=cz+ax\)

\(c^2=ax+by\).

Find all possible values of \(\frac{x}{a + x} + \frac{y}{b + y} + \frac{z}{c + z}\).

 

I'm not sure where to start. Thanks in advance!

 Dec 23, 2019
 #1
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The possible values are -1, 1, and 2.

 Dec 27, 2019
 #2
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I have no idea either CoolStuffYT    frown

 Dec 27, 2019

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