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?

Question

Mathematics

Zoey Myers

14 September, 20:22

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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Answers (1)

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Kailyn Houston · Answer 1

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