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Q. A root of the equation $\Delta=\begin{vmatrix} 0 & x-a & x-b \\ x+a & 0 & x-c \\ x+b & x+c & 0 \end{vmatrix}=0 \text { i }$

Determinants

Solution:

When we substitute $x=0, \Delta$ becomes
$\begin{vmatrix}0 & -a & -b \\a & 0 & -c \\b & c & 0\end{vmatrix}$
which is equal to 0 as $\Delta$ is skew symmetric determinant of odd order.