Find an ordered triple (x,y,z) of real numbers satisfying x ≤ y ≤ z and the system of equations
√x + √y + √z = 10
x + y + z = 42
√(xy) + √(xz) + √(yz) = 29
or, if there is no such triple, enter the word "none" as your answer.
The solution is (x,y,z) = (4,9,25).
