Question

Resolva a matriz 3x3
1 2 x
-1 x x+1 =6
3 2 6

Answer 1

EAE LUIS GUSTAVO,

BASTA APLICAR A MESMA REGRA PRA DETERMINANTE DE 3A ORDEM..

$\left|\begin{array}{ccc}1&2&x\\-1&x&x+1\\3&2&6\end{array}\right| \left\begin{array}{ccc}1&2\\-1&x\\3&2\end{array}\right=6\\\\\\ (6x)+(6x+6)-(2x)-(3x^2)-(2x-2)+12=6\\ -3x^2+8x+18=6\\ 3x^2-8x-18+6=0\\ 3x^2-8x-12=0\\\\ \Delta=(-8)^2-4\cdot3\cdot(-12)\\ \Delta=64+144\\ \Delta=208\\\\ x= \dfrac{-(-8)\pm \sqrt{208} }{2\cdot3}~\to~x= \dfrac{8\pm4 \sqrt{13} }{6}\begin{cases}x'= \dfrac{4+2 \sqrt{13} }{3}\\\\ x''= \dfrac{4-2 \sqrt{13} }{3} \end{cases}$

$\large\boxed{\boxed{S=\left\{ \dfrac{4+2 \sqrt{13} }{3}, \dfrac{4-2 \sqrt{13} }{3}\right\}}}$

Tenha ótimos estudos ;D