Question

Se A= {x E R / – x2 + 5x – 4 > 2}, então quanto vale x?

Answer 1

 Oi Amanda.

$\\ - x^2 + 5x - 4 > 2 \\ - x^2 + 5x - 6 > 0 \\ \Delta = 25 - 24 \Rightarrow \Delta = 1 \\ x = \frac{- 5 \pm \sqrt{1}}{- 2} \\\\ x = \frac{- 5 \pm 1}{- 2} \begin{cases} x'= \frac{- 5 + 1}{- 2} \Rightarrow \boxed{x' = 2} \\\\ x''= \frac{- 5 - 1}{- 2} \Rightarrow \boxed{x'' = 3}  \end{cases}$

 

Estudando os sinais...

 

 

____-____(2)____+______(3)_____-_____

 

 Portanto,

 

$\boxed{\boxed{S = \left \{ x \in \mathbb{R} / 2 < x < 3 \right \}}}$