If x, y abd z are positive with xy=24, xz=48 and yz=12, what is the value of x+y+z?
xy = 24 (1)
xz = 48 (2)
yz = 12 (3)
Divide (2) by (1) getting z / y = 2 ⇒ z = 2y
Looking at (3)
y * 2y = 12
2y^2 = 12
y^2 = 12 / 2 = 6
y = sqrt (6)
z = 2sqrt (6)
Looking at (1)
xy = 24
x * sqrt (6) = 24
x = 24 / sqrt (6) = 4sqrt (6)
So
x + y + z =
4sqrt (6) + sqrt (6) + 2sqrt (6) =
7 sqrt (6)