Question

If $a, \, b$ and $c$ are distinct positive real numbers such that $\Delta _{1}=\begin{vmatrix} a & b & c \\ b & c & a \\ c & a & b \end{vmatrix}$ and $\Delta _{2}=\begin{vmatrix} bc-a^{2} & ac-b^{2} & ab-c^{2} \\ ac-b^{2} & ab-c^{2} & bc-a^{2} \\ ab-c^{2} & bc-a^{2} & ac-b^{2} \end{vmatrix}$ , then

• A. $\Delta _{1}=\Delta _{2}$
• B. $\Delta _{1}^{2}+\Delta _{2}=0$
• C. $\Delta _{1}^{2}=\Delta _{2}$
• D. $\Delta _{1}^{2}=\Delta _{2}^{2}$

Answer 1

Answer: (C)

Elements of $\Delta _{2}$ are co-factors of the elements of $\Delta _{1}$
Hence $\Delta _{1}^{2}=\Delta _{2}$