Question

1 Determine o valor de x para que o determinante da matriz A seja igual a 12

x -3
x+2 x-2

Answer 1

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$\begin{vmatrix}\sf{x}&\sf{-3}\\\sf{x+2}&\sf{x-2}\end{vmatrix}=\sf 12$

$\sf{x^2-2x+3x+6-12=0}\\\sf{x^2+x-6=0}\\\sf \Delta=b^2-4ac\\\sf\Delta=1^2-4\cdot1\cdot(-6)\\\sf\Delta=1+24\\\sf\Delta=25$

$\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\sf x=\dfrac{-1\pm\sqrt{25}}{2\cdot1}\\\sf x=\dfrac{-1\pm5}{2}\begin{cases}\sf x_1=\dfrac{-1+5}{2}=\dfrac{4}{2}=2\\\sf x_2=\dfrac{-1-5}{2}=-\dfrac{6}{2}=-3\end{cases}$