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The number of solutions for the equation $x^{2}-5|x|+6=0$ is
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Verified Answer
The correct answer is:
$4$
We have,
$$
\begin{aligned}
x^{2}-5|x|+6 &=0 \\
|x|^{2}-5|x|+6 &=0 \\
(|x|-3)(|x|-2) &=0 \\
|x| &=3,2 \\
\Rightarrow \quad \quad x &=\pm 3, \pm 2 \\
\therefore & \text { Number of solution is } 4 .
\end{aligned}
$$
$$
\begin{aligned}
x^{2}-5|x|+6 &=0 \\
|x|^{2}-5|x|+6 &=0 \\
(|x|-3)(|x|-2) &=0 \\
|x| &=3,2 \\
\Rightarrow \quad \quad x &=\pm 3, \pm 2 \\
\therefore & \text { Number of solution is } 4 .
\end{aligned}
$$
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