Question

a+b+c=0 and a2+b2+c2 =16 find ab+bc+ca

Answer 1

$a + b + c = 0 \\ both \: side \: square... \\( a + b + c) ^{2} = {0 }^{2} \\ {a }^{2} + {b}^{2} + {c}^{2} + 2ab +2bc + 2ca = 0 \\ we \: know \: that... \\ {a}^{2} + {b}^{2} + {c }^{2} = 16 \\ so... \\16 + 2 ab+ 2 bc+ 2ca = 0 \\ 2ab + 2bc + 2ca = - 16 \\ 2(ab + \: bc + \: ca) = - 16 \\ ab + bc + ca = \frac{ - 16}{2} \\ ab + bc + ca = - 8 \: ans...$