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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Updated on: 10-Oct-2022

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