If a neq b neq c,the value of x which satisfi | vedclass

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(A) Let the given determinant be $\Delta$. We are given the equation $\Delta = 0$. Substituting $x = 0$ into the determinant,we get: $\Delta_{x=0} = \

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$x = 0$

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(A) Let the given determinant be $\Delta$. We are given the equation $\Delta = 0$. Substituting $x = 0$ into the determinant,we get: $\Delta_{x=0} = \left| \begin{array}{ccc} 0 & -a & -b \ a & 0 & -c \ b & c & 0 \end{array} ight|$ Expanding along the first row: $\Delta_{x=0} = 0(0 - (-c^2)) - (-a)(0 - (-bc)) + (-b)(ac - 0)$ $= 0 + a(-bc) - b(ac) = -abc - abc = -2abc$. Wait,let us re-evaluate the expansion: $\Delta_{x=0} = 0 - (-a)(a(0) - b(-c)) + (-b)(a(c) - b(0))$ $= a(bc) - b(ac) = abc - abc = 0$. Since the determinant equals $0$ when $x = 0$,$x = 0$ is a root of the equation.

If $a \neq b \neq c$,the 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

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