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# Algebraic system

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Assuming x, y, and z are positive real numbers satisfying

xy - z = 15

xz - y = 15

yz - x = 15

then, what is the value of xyz?

Nov 5, 2021

#1
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I do not know how many answers there may be to this.

But I said that one answer would be if they were all the same

I mean  x=y=z

then

$$x^2-x=15\\ x^2-x-15=0\\ x=\frac{1\pm \sqrt{61}}{2}\\ xyz=\left[\frac{1\pm \sqrt{61}}{2}\right]^3\\$$

Expand this out and you get 2 different answers.

Nov 5, 2021