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Question -

If a + b + c = 0 and a2 + b2 + c2 = 16, find the value of ab + be + ca.



Answer -

a + b+c = 0
Squaring both sides,
(a + b + c)2 = 0
a2 +b2 + c2 + 2(ab + bc + ca) = 0
16 + 2(ab + bc + c) = 0
2(ab +bc + ca) = -16
 ab + bc + ca =-162 =-8
ab +bc + ca = -8

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