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
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