If \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2
FURTHER MATHEMATICS
WAEC 2018
If \(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24 \), find the values of x.
Explanation
\(\begin{vmatrix} x - 3 & -4 & 3 \\ 5 & 2 & 2 \\ 2 & -4 & 6 - x \end{vmatrix} = -24\)
\((x - 3)[2(6 - x) + 8] + 4[5(6 - x) - 4] + 3[- 20 - 4] = -24\)
\((x - 3)[12 - 2x + 8] + 4[30 - 5x - 4] + 3[-24] = -24\)
\((x - 3)(20 - 2x) + 4(26 - 5x) - 72 = -24\)
\((x - 3)(20 - 2x) + 4(26 - 5x) = - 24 + 72 = 48\)
\(20x - 2x^{2} - 60 + 6x + 104 - 20x = 48\)
\(-2x^{2} + 6x - 4 = 0\)
\(2x^{2} - 6x + 4 = 0\)
Solving the equation, we get x = 1 or 2.
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