If a + b + c = 0 and a2 + b2 + c2
Question:

If $a+b+c=0$ and $a^{2}+b^{2}+c^{2}=16$, find the value of $a b+b c+c a$ :

Solution:

We know that,

$\left[\because(a+b+c)^{2}=a^{2}+b^{2}+c^{2}+2 a b+2 b c+2 c a\right]$

$(0)^{2}=16+2(a b+b c+c a)$

$2(a b+b c+c a)=-16$

$a b+b c+c a=-8$

Hence, value of required express ab + bc + ca = – 8