Question

Quais São As Raízes da Equação x2+ 3x-18=0

Answer 1

Olá.

Usaremos o teorema de Pitágoras para resolver essa equação.
Usando a fórmula ax+bx+c=0, os coeficiente são:
$\Large\left\{\begin{array}{llc}\mathsf{a}&=&1\\\mathsf{b}&=&3\\\mathsf{c}&=&-18\end{array}$

Vamos montar no teorema:
$\Large\begin{array}{l} \mathsf{x=\dfrac{-b\pm\sqrt{b^2-4\cdot a\cdot c}}{2\cdot a}}\\\\\\ \mathsf{x=\dfrac{-3\pm\sqrt{3^2-4\cdot1\cdot(-18)}}{2\cdot1}}\\\\\\ \mathsf{x=\dfrac{-3\pm\sqrt{9-4\cdot(-18)}}{2}}\\\\\\ \mathsf{x=\dfrac{-3\pm\sqrt{9+72}}{2}}\\\\\\ \mathsf{x=\dfrac{-3\pm\sqrt{81}}{2}}\\\\\\ \mathsf{x=\dfrac{-3\pm9}{2}}\\\\\\ \end{array}$


Vamos descobrir os dois valores possíveis por x:
$\Large\begin{array}{l}\mathsf{x'=\dfrac{-3+9}{2}}\\\\ \mathsf{x'=\dfrac{6}{2}}\\\\ \mathsf{x'=3}\\\\\\ \mathsf{x''=\dfrac{-3-9}{2}}\\\\ \mathsf{x''=\dfrac{-12}{2}}\\\\ \mathsf{x''=-6}\\\\\\ \boxed{\mathsf{S=\{x\in \mathbb{N}~|~-6,~3\}}}\end{array}$

Qualquer dúvida, deixe nos comentários.
Bons estudos.