If $ab + bc + ca = 0$ and $\left| {\,\begin{array}{*{20}{c}}{a - x}&c&b\\c&{b - x}&a\\b&a&{c - x}\end{array}\,} \right| = 0$, then one of the value of $x$ is
If $ab + bc + ca = 0$ and $\left| {\,\begin{array}{*{20}{c}}{a - x}&c&b\\c&{b - x}&a\\b&a&{c - x}\end{array}\,} \right| = 0$, then one of the value of $x$ is
- A
${({a^2} + {b^2} + {c^2})^{\frac{1}{2}}}$
- B
${\left[ {\frac{3}{2}({a^2} + {b^2} + {c^2})} \right]^{\frac{1}{2}}}$
- C
${\left[ {\frac{1}{2}({a^2} + {b^2} + {c^2})} \right]^{\frac{1}{2}}}$
- D
None of these
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- [IIT 2016]
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