Question

If $a\ne b\ne c,$ are value of x which satisfies the equation $\left|\begin{array}{ccc}0& x-a& x-b\\ x+a& 0& x-c\\ x+b& x+c& 0\end{array}\right|=0$ is given by

• A. $x=0$
• B. $x=c$
• C. $x=b$
• D. $x=a$

Answer 1

The correct option is A $x=0$

$\left|\begin{array}{ccc}0& x-a& x-b\\ x+a& 0& x-c\\ x+b& x+c& 0\end{array}\right|=0$
$\Rightarrow (x-a)(x+b)(x-c)+(x-b)(x+a)(x+c)=0$

We can now check by options
$foroptionA,$ put $x=0$ in above equation we get,

$\Rightarrow (0-a)(0+b)(0-c)+(0-b)(0+a)(0+c)=0$

$\Rightarrow abc-abc=0$

So, $x=0$ satisfies the equation.