We have:

(1) x²yz = 12      (2) xy²z = 6       (3) xyz² = 18

The ratio of (1) to (2) is: x²yz/xy²z = 12/6 from which we get: y = x/2

The ratio of (1) to (3) is: x²yz/xyz² = 12/18 from which we get: z = 3x/2

The product of (1), (2) and (3) is:

(x²yz)(xy²z)(xyz²) = (12)(6)(18)                                    

from which we get: x⁴y⁴z⁴ = 1296  or: (xyz)⁴ = 6⁴ Hence, xyz = 6.

Substituting the previous values,we get:

(x)(x/2)(3x/2) = 6  or :

3x³/4 = 6 Hence, x = 2, and y = x/2 = 1,z = 3x/2 = 3 The solutions are (x,y,z) = (2, 1, 3) or (-2, -1, -3).

View different answers : radagast | Soarer|Mark Morse