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If $a + b + c = 0$ and $a^2 + b^2 + c^2 = 16$, find the value of $ab + bc + ca$.
Given:
$a + b + c = 0$ and $a^2 + b^2 + c^2 = 16$
To do:
We have to find the value of $ab + bc + ca$.
Solution:
We know that,
$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$
Therefore,
$a + b+ c = 0$
Squaring both sides, we get,
$(a + b + c)^2 = 0$
$a^2 + b^2 + c^2 + 2ab + 2bc + 2ca = 0$
$16 + 2(ab + bc + ca) = 0$
$2(ab + bc + ca) = -16$
$ab + bc + ca =-8$
Hence, the value of $ab + bc + ca$ is $-8$.
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