Question

Resolva em ℝ
(a) (2X − 5 )+ [x + 3] = 0
(b) x^3 − 2x^2 = 5x

Answer 1

Vamos lá :

a) (2x - 5) + [x + 3] = 0
     2x - 5 + x + 3 = 0
     3x - 2 = 0
     3x = 2
       x = 2/3

b) x³- 2x² = 5x
    x³ - 2x² - 5x = 0
    x . (x² - 2x - 5) = 0

x' = 0

ou 

x² - 2x - 5 = 0

a = 1 ; b = - 2 ; c = - 5

Δ = b² - 4ac
Δ = (-2)² - 4.1.(-5)
Δ = 4 - 4.(-5)
Δ = 4 + 20
Δ = 24        ⇒⇒⇒√Δ = 2√6

Aplica a formula de Bhaskara ...

x = - b +/- √Δ / 2.a
x = - (- 2) +/- 2√6 / 2.1
x = 2 +/- 2√6 / 2

x'' = 2 + 2√6 / 2   ⇒⇒ x'' = 1 + √6
x''' = 2 - 2√6 / 2   ⇒⇒ x''' = 1 - √6

S = {1 - √6,0,1 + √6}

Espero ter ajudado !!!