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?
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.