Question:
Using properties of determinants prove that:
$\left|\begin{array}{lll}x-3 & x-4 & x-\alpha \\ x-2 & x-3 & x-\beta \\ x-1 & x-2 & x-\gamma\end{array}\right|=0$, where $\alpha, \beta, y$ are in AP.
Solution:
$=0$
Hence proved
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