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.
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1 + 4 + 5 = 10
1 + 16 + 25 = 42
√(1*16) + √(1*25) + √(16*25) = 29
x = 1 y = 16 z = 25
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