Question

qual o conjunto da solução da inequação
 /2   x     x/ 
 /1    1    0/ < 0
 /x    0    1/

Answer 1

Oi Catarina,

aplique a regra de Sarruz:

$\left|\begin{array}{ccc}2&x&x\\1&1&0\\x&0&1\end{array}\right| \left\begin{array}{ccc}2&x\\1&1\\x&0\end{array}\right~<~0~~~~.\\\\\\ 2+0+0-x^2+0-x<0\\ -x^2-x+2<0\\\\(multiplique~por~-1~e~troque~o~sinal~da~desigualdade)~~~~~~~~.\\\\ x^2+x-2>0$

$\Delta=b^2-4ac\\ \Delta=1^2-4\cdot1\cdot(-2)\\ \Delta=1+8\\ \Delta=9\\\\ x= \dfrac{-b\pm \sqrt{\Delta} }{2}= \dfrac{-1\pm \sqrt{9} }{2\cdot1}= \dfrac{-1\pm3}{2}\begin{cases}x'= \dfrac{-1+3}{2}= \dfrac{2}{2}=1\\\\ x''= \dfrac{-1-3}{2}= \dfrac{-4}{2}=-2 \end{cases}\\\\\\ \Large\boxed{\boxed{S=\{x\in\mathbb{R}~|~1>x<-2\}}}.\\.$

Tenha ótimos estudos ^^