Question

Determinante de ordem 2

Answer 1

$\left[\begin{array}{ccc}x-2&2\\2x-3&x\end{array}\right]= \left[\begin{array}{ccc}1&16\\1&1\end{array}\right] \Rightarrow x(x-2)-2(2x-3)=1-16 \Rightarrow \\ \\ \\ x^2-2x-4x+6=15 \Rightarrow x^2-6x-9=0 \\ \\ \Delta=(-6)^2-4(1)(-9)=36+36=72 \\ \\ \sqrt{\Delta} = \sqrt{72} = \sqrt{2*36} =6 \sqrt{2} \\ \\ x_1= \frac{-(-6)+6 \sqrt{2}}{2(1)} =3+3 \sqrt{2} \\ \\ x_2= \frac{-(-6)-6 \sqrt{2}}{2(1)} =3-3 \sqrt{2} \\ \\ Resposta{:} \\ x=3+3 \sqrt{2}\,\, ou\,\, 3-3 \sqrt{2}$