Question

Equações de segundo grau
a) x²+x (x-6)=0
b) x (x+3)=5x
c) x (x-3)-2 (x-3)=6
d) (x+5)² = 25
e) (x-2)²=4-9x
f) (x+1)(x-3)=-3

Answer 1

a) x²+x (x-6)=0
x² + x² - 6x = 0
2x² - 6x = 0 ÷ (2)
x² - 3x = 0
x.(x - 3) = 0
x = 0
(x - 3) = 0
x - 3 = 0
x = + 3

S[0 ; 3]


b) x (x+3)=5x
x² + 3x - 5x = 0
x² - 2x = 0
x.(x - 2) = 0
x = 0
(x - 2) = 0
x - 2 = 0
x = + 2

[0 ; 2]


c) x (x-3)-2 (x-3)=6
x² - 3x - 2x + 6 - 6 = 0      cancela + 6 - 6
x² - 5x = 0
x.(x - 5) = 0
x = 0
(x - 5) = 0
x - 5 = 0
x = + 5

S[0 ; 5]


d) (x+5)² = 25
(x + 5).(x + 5) = 25
x² + 5x + 5x + 25 - 25 = 0       cancela + 25 - 25
x² + 10x  = 0
x.(x + 10) = 0
x = 0
(x + 10) = 0
x + 10 = 0
x = - 10

S[0 ; -10]


e) (x-2)²=4-9x
(x - 2).(x - 2) = 4 - 9x
x² - 2x - 2x + 4 - 4 + 9x = 0 
x² - 2x- 2x + 9x + 4 - 4=0      cancela + 4 - 4
x² - 4x + 9x = 0
x² + 5x = 0
x.(x + 5) = 0
x = 0
(x + 5) = 0
x + 5 = 0
x = - 5

S[0 ; - 5]



f) (x+1)(x-3)=-3
x² - 3x + x - 3 + 3 = 0         elimina  - 3 + 3
x² - 2x = 0
x.(x - 2) = 0
x = 0
(x - 2) = 0
x - 2 = 0
x = + 2

S[0 ;  2]