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please prove the given relation using determinant operations.....

please prove the given relation using determinant operations.....

Question Image
Grade:12

1 Answers

mycroft holmes
272 Points
4 years ago
The given determinant can be written as 
 
\begin{vmatrix} b & c & a\\ c & a & b\\ a & b & c \end{vmatrix} \times \begin{vmatrix} c & a & b\\ b & c & a\\ -a & -b & -c \end{vmatrix}
 
both of which are easily proved as equal to 3abc-a^3-b^3-c^3
 
Hence given determinant equals (a^3+b^3+c^3-3abc)^2
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