If x, y, and z are positive with xy = 20, xz = 35, and yz = 14, then what is xyz?
xy = 20 ⇒ y = 20/x
xz = 35 ⇒ z = 35 /x
yz = 14
So
(20/x) (35/x) = 14
700 = 14 x^2
700 / 14 = x^2
x^2 = 50
x= 5sqrt (2)
y = 20 / [ 5sqrt 2] = 4 / sqrt 2
z= 35 / [ 5sqrt 2] = 7 /sqrt 2
xyz = 5sqrt 2 * 4 /sqrt 2 * 7/ sqrt 2 = 140 / sqrt 2 = 70sqrt 2
