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If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :

10
30
50
70

Correct Answer: 50

Explanation:

$a + b + c 2 = a 2 + b 2 + c 2 + 2 a b + b c + c a$

$2 a b + b c + c a = a + b + c 2 - a 2 + b 2 + c 2 = 169 - 69 = 100 = a b + b c + c a = 50$

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