Final answer:
To solve for xyz, we can use the given information of xy = 8, xz = 5, yz = 10. By substituting the values of x and z into the equation yz = 10, we can solve for y and obtain two solutions, y = 4 or y = -4. Substituting these values back into the equations for x and z, we find that the solutions for xyz are xyz = 20 or xyz = -20.
Step-by-step explanation:
To solve for xyz, we can use the given information: xy = 8, xz = 5, yz = 10.
We want to find xyz. From the given equations, we can see that xy = 8, so x = 8/y. Next, we substitute this value of x into the equation xz = 5, giving us (8/y)z = 5. Rearranging this equation, we get z = (5y)/8. Finally, we substitute the values of x and z into the equation yz = 10, giving us y[(5y)/8] = 10. Simplifying this equation, we get y^2 = 16, which means y = 4 or y = -4. Substituting these values back into the equations for x and z, we find that x = 2 and z = 5/2 or x = -2 and z = -5/2. Therefore, the solutions for xyz are xyz = 2 * 4 * (5/2) = 20 or xyz = -2 * -4 * (-5/2) = -20.