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If $a^2 + b^2 + c^2 = 16$ and $ab + bc + ca = 10$, find the value of $a + b + c$.
Given:
$a^2 + b^2 + c^2 = 16$ and $ab + bc + ca = 10$
To do:
We have to find the value of $a + b + c$.
Solution:
We know that,
$(a+b+c)^2=a^2+b^2+c^2+2ab+2bc+2ca$
Therefore,
$(a + b + c)^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca$
$= 16 + 2 (ab+bc+ca)$
$=16+2\times10$
$= 16 + 20$
$= 36$
$= 6^2$
$\Rightarrow (a+b+c)=\sqrt{6^2}$
$=\pm 6$
Hence, the value of $a + b + c$ is $\pm 6$.
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