If \[a,b,c\] are positive integers, then the determinant \[\Delta =\left| \,\begin{matrix} {{a}^{2}}+x & ab & ac \\ ab & {{b}^{2}}+x & bc \\ ac & bc & {{c}^{2}}+x \\ \end{matrix}\, \right|\] is divisible by

\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]

If \[a,b,c\] are positive integers, then the determinant \[\Delta =\le

1.	If \[a,b,c\] are positive integers, then the determinant \[\Delta =\left\| \,\begin{matrix} {{a}^{2}}+x & ab & ac \\ ab & {{b}^{2}}+x & bc \\ ac & bc & {{c}^{2}}+x \\ \end{matrix}\, \right\|\] is divisible by
A.	\[{{x}^{3}}\]
B.	\[{{x}^{2}}\]
C.	\[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]
D.	None of these
Answer» C. \[({{a}^{2}}+{{b}^{2}}+{{c}^{2}})\]

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If \[a,b,c\] are positive integers, then the determinant \[\Delta =\left| \,\begin{matrix} {{a}^{2}}+x & ab & ac \\ ab & {{b}^{2}}+x & bc \\ ac & bc & {{c}^{2}}+x \\ \end{matrix}\, \right|\] is divisible by

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