a)
x² - 5x + 4 > 0
Δ = b² - 4ac = (-5)² -4 * 1 * 4 = 25 - 16 = 9
√Δ = √9 = 3
[tex]x_1 = \frac{-b-3 }{2*1} = \frac{5-3}{2} = \frac{2}{2} = 1 \\x_2 = \frac{-b+3 }{2*1} = \frac{5+3}{2} = \frac{8}{2} = 4[/tex]
a > 0
x ∈ (-∞ , 1) u (4, +∞)
b)
-x(x+6)<9
-x² - 6x - 9 < 0
Δ = b² - 4ac = (-6)² - 4 * (-1) * (-9) = 36 -36 = 0
√Δ = √0 = 0
[tex]x_1 = \frac{-b-0 }{2*(-1)} = \frac{6-0}{-2} = \frac{6}{-2} = -3 \\x_2 = \frac{-b+0 }{2*(-1)} = \frac{6+0}{-2} = \frac{6}{-2} = -3[/tex]
a < 0
x ∈ (-∞ , -3) u (-3, +∞)
