If \(\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=k a^{2} b^{2} c^{2}\), then \(k=\)

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If \(\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=k a^{2} b^{2} c^{2}\), then \(k=\)

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kritika · Answer 1 · 2021-12-26T14:47:02+0000

Ans: (D)
Hint : \(\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=(a b c)\left|\begin{array}{ccc}a & c & a+c \\ a+b & b & a \\ b & b+c & c\end{array}\right|\) opening through \(R-1=4 a^{2} b^{2} c^{2}\)

If \(\left|\begin{array}{ccc}a^{2} & b c & c^{2}+a c \\ a^{2}+a b & b^{2} & c a \\ a b & b^{2}+b c & c^{2}\end{array}\right|=k a^{2} b^{2} c^{2}\), then \(k=\)

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