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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?

 May 3, 2022
 #1
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Since xy - z = xz - y = 15, \((xy - z) - (xz - y) = 15 -15 = 0\).

Then \(x(y - z) + (y - z) = 0\).

Factorizing gives \((x + 1)(y - z) = 0\).

 

Since x is positive, it is not possible that x + 1 = 0. The only possibility is y - z = 0, which implies y = z.

 

Similarly, we can get x = z from equation 1 and equation 3. Therefore, \(x = y = z\).

 

Substituting that into xy - z = 15 gives \(x^2 - x = 15\). You can solve it and get the positive value of x. Then since x = y = z, xyz is just x^3. Please try to continue from here.

 May 3, 2022

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