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| 1. |
| a² bc c² + ac || a² + ab b² Ca |= 4a²b²c²| ab b² + bc c² | |
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Answer» |(a2, bc, ac+c2)(a2+ab,b2, ac(ab, b2+bc, c2)| = 4a2b2c2 \(\Delta=\begin{vmatrix}a^2&bc&ac+c^2\\a^2+ab&b^2&ac\\ab&b^2+bc&c^2\end{vmatrix}\) Taking a, b and c common from C1, C2 and C3 respectively. \(=abc\begin{vmatrix}a&c&a+c\\a+b&b&a\\b&b+c&a\end{vmatrix}\) Using C1 → C1 + C2 - C3 \(=abc\begin{vmatrix}0&c&a+c\\2b&b&a\\b&b+c&c\end{vmatrix}\) Using R2 → R2 - R3 \(=abc\begin{vmatrix}0&c&a+c\\0&-c&a-c\\2b&b+c&c\end{vmatrix}\) Expanding along C1, ∆ = abc[0 - 0 + 2b(ca - c2 + ca + c2)] or ∆ = abc(4abc) or ∆ = 4a2b2c2 |
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