Question

Encontre as raízes solução do sistema​

Answer 1

Resposta:

$\sf \displaystyle \left\{ \begin{aligned} \sf x & \sf = 2y \\ \sf x + y^2 & \sf = 35 \end{aligned} \right$

Aplicar o método da substituição:

$\sf \displaystyle x + y^{2} = 35$

$\sf \displaystyle 2y + y^{2} = 35$

$\sf \displaystyle y^{2} + 2y - 35 = 0$

$\sf \displaystyle \Delta = b^2 -\:4ac$

$\sf \displaystyle \Delta = 2^2 -\:4\cdo 1 \cdot (-\: 35)$

$\sf \displaystyle \Delta = 4 +140$

$\sf \displaystyle \Delta = 144$

$\sf \displaystyle y = \dfrac{-\,b \pm \sqrt{ \Delta } }{2a} = \dfrac{-\,2 \pm \sqrt{ 144} }{2\cdot 1} = \dfrac{-\,2 \pm 12}{2} \Rightarrow\begin{cases} \sf y_1 = &\sf \dfrac{-\,2 + 12}{2} = \dfrac{10}{2} = \;5 \\\\ \sf y_2 = &\sf \dfrac{-\,2 - 12}{2} = \dfrac{- 14}{2} = - 7\end{cases}$

Determinar o valor de y:

$\sf \displaystyle x_1 = 2y_1$

$\sf \displaystyle x_1 = 2 \cdot 5$

$\sf \displaystyle x_1 = 10$

$\sf \displaystyle x_2 = 2y_2$

$\sf \displaystyle x_2 = 2 \cdot (-\; 7)$

$\sf \displaystyle x_2 = -\:14$

$\boldsymbol{ \sf \displaystyle S=\left\lbrace \left({x}_{1},{y}_{1}\right);\left({x}_{2},{y}_{2}\right)\right\rbrace =\left\lbrace \left(\mathrm{ 10, 5 }\right);\left( -\; 14, -\: 7 \right)\right\rbrace }$

Explicação passo-a-passo: