TS EAMCET · Maths · Determinants
If \(\Delta_1=\left|\begin{array}{lll}1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3\end{array}\right|\) and \(\Delta_2=\left|\begin{array}{lll}b c & b+c & 1 \\ c a & c+a & 1 \\ a b & a+b & 1\end{array}\right|\), then \(\frac{\Delta_1}{\Delta_2}=\)
- A \(a b+b c+c a\)
- B \(a b c\)
- C \(2(a b+b c+c a)\)
- D \((a+b+c)^2\)
Answer & Solution
Correct Answer
(A) \(a b+b c+c a\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { (a) } \Delta_1=\left|\begin{array}{lll} 1 & a^2 & a^3 \\ 1 & b^2 & b^3 \\ 1 & c^2 & c^3 \end{array}\right| \\ & R_2 \rightarrow R_2-R_1, R_3 \rightarrow R_3-R_1 \\ & =\left|\begin{array}{ccc} 1 & a^2 & a^3 \\ 0 & b^2-a^2 & b^3-a^3 \\ 0 & c^2-a^2 &…
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