Practicing Success
If $\begin{vmatrix} a+x & a-x & a-x\\a-x&a+x & a-x\\a-x&a-x&a+x\end{vmatrix}=0$ then the values of x are : |
0, a a, 2a 0, 3a 0, 2a |
0, 3a |
The correct answer is Option (3) → 0, 3a $\begin{vmatrix} a+x & a-x & a-x\\a-x&a+x & a-x\\a-x&a-x&a+x\end{vmatrix}$ $C_1→C_1+C_2+C_3$ $\begin{vmatrix} 3a-x & a-x & a-x\\3a-x&a+x & a-x\\3a-x&a-x&a+x\end{vmatrix}$ $⇒(3a-x)\begin{vmatrix} 1 & a-x & a-x\\1&a+x & a-x\\1&a-x&a+x\end{vmatrix}$ so $R_2→R_2-R_1$, $R_3→R_3-R_1$ $(3a-x)\begin{vmatrix} 1 & a-x & a-x\\2&2x & 0\\0&0&2x\end{vmatrix}=0$ $⇒4x^2(3a-x)=0$ $⇒x=0,3a$ |