If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca : 10 30 50 70 a + b +

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Question
If a + b + c = 13, a2+b2+c2=69 then find the ab + bc + ca :
Options
A. 10
B. 30
C. 50
D. 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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