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Question

If the sum of the squares of nonnegative real numbers a,b, and c is 13, and ab + bc + ca = 6, then what is the sum of a,b, and c?

Accepted Answer

Since (a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = (13) + 2(6) = 25, it follows that a+b+c = 5. Since a,b,c 0 we find a+b+c=5.