Question

if a+b+c=0 and a^2+b^2+c^2=16. find the value of ab + bc+ ca

Answer 1

answer is -8

use (a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ca)

Answer 2

$( {a + b + c)}^{2} = {a}^{2} + {b }^{2} + {c}^{2} + 2ab + 2bc + 2ca \\ 0 = 16 + 2(ab + bc + ca) \\ab + bc + ca = - 16 \div 2 = - 8$