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If an angular bisector of the coordinate axes is one of the lines of $x^2+2 a x y+3 y^2=0$, then sum of all possible values of $a$ is
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Bisectors of the angle between the coordinate axes are $y= \pm x$
Then, $x^2+2 a x( \pm x)+3 x^2=0$
$\begin{array}{ll}
\Rightarrow & 1 \pm 2 a+3=0 \Rightarrow \pm 2 a=-4 \\
\Rightarrow & \quad a=\frac{-4}{2}, \frac{-4}{-2} \Rightarrow a=-2,2 \\
\therefore & \text { Sum }=0
\end{array}$
Then, $x^2+2 a x( \pm x)+3 x^2=0$
$\begin{array}{ll}
\Rightarrow & 1 \pm 2 a+3=0 \Rightarrow \pm 2 a=-4 \\
\Rightarrow & \quad a=\frac{-4}{2}, \frac{-4}{-2} \Rightarrow a=-2,2 \\
\therefore & \text { Sum }=0
\end{array}$
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