Question

Resolva ,graficamente a seguinte inequaçao x²-2x-3>0​

Answer 1

Resposta:

$\sf x^2-2x-3 > 0$

$\sf x^2-2x-3 = 0$

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

$\sf \Delta = (-2)^2 -\:4 \cdot 1 \cdot (-3)$

$\sf \Delta = 4 + 12$

$\sf \Delta = 16$

$\sf x = \dfrac{-\,b \pm \sqrt{ \Delta } }{2a} = \dfrac{2 \pm \sqrt{ 16 } }{2 \cdot 1} = \dfrac{2 \pm 4 }{2} \Rightarrow\begin{cases} \sf x_1 = &\sf \dfrac{2 + 4}{2} = \dfrac{6}{2} = \;3 \\\\ \sf x_2 = &\sf \dfrac{2 - 4}{2} = \dfrac{- 2}{2} = - 1\end{cases}$

$\boldsymbol{ \sf \displaystyle S=\{x\in\mathbb{R}\mid x < - 1 \text{ ou }x > 3 \}=]-\infty,-1 [\cup ]3,+\infty [ }$

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