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?
+9675 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 x2−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.
