Question

resolva em R, a equação |1  -2  0|
                                     |3  x   1| = 13
                                     |2  1   x|

Answer 1

E aí Alexandre,

aplicando a regra de Sarruz, teremos:

$\left|\left|\begin{array}{ccc}1&-2&0\\3&~~x&1\\2&~~1&x\end{array}\right|\right| \left\begin{array}{ccc}1&-2\\3&~~x\\2&~~1\end{array}\right =13\\\\\\ x^2-4+0-0-1+6x=13\\ x^2-4-1+6x=13\\ x^2+6x-4-1-13=0\\ x^2+6x-18=0\\\\ \Delta=6^2-4*1*(-18)\\ \Delta=36+72\\ \Delta=108\\\\ x= \dfrac{-6\pm \sqrt{108} }{2*1}= \dfrac{-6\pm2 \sqrt{27} }{2}=-3\pm \sqrt{27}\\\\\\ \boxed{S=\left\{-3+ \sqrt{27},-3- \sqrt{27}\right\}}$

Tenha ótimos estudos =))