Question

Dada a equação |x² -2x-4|=4, a soma dos elementos do conjunto solução é:

Answer 1

$\large\boxed{\begin{array}{l}\rm| x^2-2x-4|=4\\\rm x^2-2x-4=4\\\rm x^2-2x-4-4=0\\\rm x^2-2x-8=0\\\rm\Delta=b^2-4ac\\\rm\Delta=(-2)^2-4\cdot1\cdot(-8)\\\rm\Delta=4+32\\\rm\Delta=36\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-(-2)\pm\sqrt{36}}{2\cdot1}\\\\\rm x=\dfrac{2\pm6}{2}\begin{cases}\rm x_1=\dfrac{2+6}{2}=\dfrac{8}{2}=4\\\\\rm x_2=\dfrac{2-6}{2}=-\dfrac{4}{2}=-2\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\rm x^2-2x-4=-4\\\rm x^2-2x-4+4=0\\\rm x^2-2x=0\\\rm x\cdot(x-2)=0\\\rm x=0\\\rm x-2=0\\\rm x=2\\\rm S=\{-2,0,2,4\}\\\underline{\boldsymbol{soma\,das\,ra\acute izes:}}\\\rm \sum=-\diagup\!\!\!2+0+\diagup\!\!\!2+4=4\\\rm \sum\longrightarrow s\acute imbolo\,de\,somat\acute orio\end{array}}$