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If the sum of the squares of nonnegative real numbers a,b, and c is 39, and ab + bc + ca = 21, then what is the sum of a,b, and c?

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devishri1977

Answer:

Step-by-step explanation:

a² + b² + c² = 39

ab + bc + ca = 21

(a + b + c)² = a² + b² +c² + 2[ab + bc +ca]

(a + b + c)² = 39 + 2*21

                 = 39 + 42

(a+ b + c)² = 81

a +b + c = √81 = √9*9

a + b + c = 9

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