Question

encontre as raizes reais das equacoes

a) x(x+3)=5x+15
b) (x+4)^2=9x+22

Answer 1

A) x(x + 3) = 5x + 15
x² + 3x = 5x + 15
x² + 3x - 5x - 15
x² - 2x - 15

∆ = b² - 4ac
∆ = (-2)² - 4.1.(-15)
∆ = 4 + 60
∆ = 64


x = -b±√∆/2a

x¹ = 2 + 8/2
x¹ = 10/2
x¹ = 5


x² = 2 - 8/2
x² = -6/2
x² = -3.


B) (x + 4)² = 9x + 22
(x + 4)(x + 4) = 9x + 22
x² + 4x + 4x + 16 = 9x + 22
x² + 16x + 16 = 9x + 22
x² + 16x - 9x + 4 = 22
x² + 5x + 16 - 22
x² + 5x - 6

∆ = b² - 4ac
∆ = 5² - 4.1.(-6)
∆ = 25 + 24
∆ = 49


x = -b±√∆/2a

x¹ = -5 + 7/2
x¹ = 2/2
x¹ = 1

x² = -5 - 7/2
x² = -12/2
x² = -6