Question

If $\left|\begin{array}{ccc}x& 2& 8\\ 2& 8& x\\ 8& x& 2\end{array}\right|=\left|\begin{array}{ccc}3& x& 7\\ x& 7& 3\\ 7& 3& x\end{array}\right|=\left|\begin{array}{ccc}5& 5& x\\ 5& x& 5\\ x& 5& 5\end{array}\right|=0$ then $x$ is equal to

• A. $0$
• B. $-10$
• C. $3$
• D. None of these

Answer 1

Answer: (B)

$-10$

On applying $R_1\to R_1+R_2+R_3$ in each determinant, we can take out $(x+10)$ common.
Then, we get $x+10=0$
$\Rightarrow x=-10$