Without expanding the determinant, prove that: Show that \( x=2 \) is a root of the equation \( ...

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Without expanding the determinant, prove that:
Show that \( x=2 \) is a root of the equation \( \left|\begin{array}{ccc}x & -6 & -1 \\ 2 & -3 x & x-3 \\ -3 & 2 x & 2+x\end{array}\right|=0 \).
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