Question

Tentei de tudo e não consigo resolver essa.

Answer 1

$\Large\displaystyle\begin{gathered}\left|\begin{array}{ccc}x&2&-1\\-3&6&1\\9&x&-5\end{array}\right|=14 \end{gathered}$

$\Large\displaystyle\begin{gathered}\left|\begin{array}{ccc}x&2&-1\\-3&6&1\\9&x&-5\end{array}\right|\left|\begin{array}{ccc}x&2\\-3&6\\9&x\end{array}\right|=14 \end{gathered}$

$\Large\displaystyle\begin{gathered}-30x+18+3x-(-54+x^2+30)=14 \end{gathered}$

$\Large\displaystyle\begin{gathered}-30x+18+3x+54-x^2-30=14 \end{gathered}$

$\Large\displaystyle\begin{gathered}-x^2-27x+42=14 \end{gathered}$

$\Large\displaystyle\begin{gathered}-x^2-27x+28=0 \end{gathered}$

$\Large\displaystyle\begin{gathered}\Delta= b^4 -4ac \end{gathered}$

$\Large\displaystyle\begin{gathered}\Delta= 841 \end{gathered}$

$\Large\displaystyle\text{ \begin{gathered}x_{1,2}= \frac{27\pm\sqrt{841} }{-2} \implies \begin{cases}x_1=-28\\ x_2= 1\end{cases}\end{gathered} }$

$\Large\displaystyle\begin{gathered}S=\{-28,1\} \end{gathered}$