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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┬а= 0
тЗТ a2┬а+b2┬а+ c2┬а+ 2(ab + bc + ca) = 0
16 + 2(ab + bc + c)┬а=┬а0
тЗТ 2(ab +bc + ca) = -16
тЗТ┬аab + bc + ca =-162┬а=-8
тИ┤ ab +bc + ca = -8

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