5 ) resolva as equaçoes
a) x²-2x = 0
b) x² + 5x = 0
c) 3x² - x = 0
d) 2x² + x = 0
e ) - x² + 4x = 0
f) -2x² - 7x = 0
g) 4x² - 5x = 0
h) 3x² + 7x = 0
i) x² + 2x = 0
4 3
j) x ² = 5x
k) 3x = 6x²
l ) 5x² = 3x
m) (x+2)² = 4
n) (2x +1)² = (3x-1) ( 5x-1)
o) (2x-3) ( x+4) = (x+2) ( 5x -6)

1

Respostas

2014-07-16T21:29:18-03:00
5 ) resolva as equaçoes 
a) x²-2x = 0 
X² - 2X = 0   por em evidencia
x(x - 2) = 0
x₁ = 0
e
(x-2) =
x - 2 = 0
x₂ = 2 


b) x² + 5x = 0 
x² + 5x = 0
x(x + 5) = 0
x₁ = 0
e
(x+ 5) = 0
x+5 = 0
x₂ = - 5


c) 3x² - x = 0 

3x² - x = 0
x(3x - 1) = 0
x₁ = 0
e
(3x-1) = 0
3x-1=0
3x = + 1
x₂ = 1/3


d) 2x² + x = 0 
2x² + x = 0
x(2x + 1) = 0
x₁ = 0
e
(2x + 1) = 0
2x + 1 = 0
2x = - 1
x₂ = - 1/2


e ) - x² + 4x = 0 

-x² + 4x = 0
x(-x + 4) = 0
x₁ = 0
e
(-x+4) = 0
-x + 4 = 0
-x = - 4
x = (-)(-)4
x₂=   + 4


f) -2x² - 7x = 0

-2x² - 7x = 0
x(-2x - 7) = 0
x₁ = 0
e
(-2x - 7 )=0
-2x - 7 = 0
-2x = + 7
x = 7/-2
x₂ = - 7/2 


g) 4x² - 5x = 0 

4x² - 5x = 0
x(4x - 5) = 0
x₁ = 0
e
(4x - 5) = 0
4x - 5 = 0
4x = 5
x₂ = 5/4


h) 3x² + 7x = 0 

3x² + 7x = 0
x(3x + 7) = 0
x₁₁= 0
e
(3x + 7)=0
3x + 7 = 0
3x = - 7
x₂ = - 7/3


i) x² + 2x = 0 
    4      3

3x² + 8x = 0
-------------------
       12

3x² + 8x = 0
x(3x + 8) = 0
x₁ = 0
e
(3x+8)= =
3x + 8 = 0
3x = - 8
x₂ = - 8/3

j) x ² = 5x 

x² = 5x
x² - 5x = 0
x(x - 5) = 0
x₁ = 0
e
(x-5) = 0
x - 5 = 0
x₂ = + 5

k) 3x = 6x²
3x = 6x²
3x - 6x² = 0
3x(1 - 2x) = 0
3x = 0
x = 0/3
x₁ = 0
e
(1-2x) = 0
1 - 2x = 0
-2x = - 1
x = -1/-2
x₂ = + 1/2 


l ) 5x² = 3x 
5x² = 3x
5x² - 3x= 0
x(5x - 3) = 0
x₁= 0
e
(5x-3) = 0
5x - 3 = 0
5x = +3
x₂ = 3/5


m) (x+2)² = 4
(x+2)² = 4
(x+2)(x+2) = 4
x² + 2x + 2x + 4 = 4
x² + 4x + 4 = 4 
x² + 4x + 4 - 4 = 0
x² + 4x + 0 = 0
x² + 4x = 0
x(x + 4 )=0
x₁ = 0
e
(x+ 4) = 0
x + 4 = 0
x₂₂ = - 4


n) (2x +1)² = (3x-1) ( 5x-1)

(2x + 1)²       = (3x-1)(5x-1)
(2x+1)(2x+1)      = (3x-1)(5x-1)
4x² + 2x +2x + 1 = 15x² - 3x - 5x + 1
4x² + 4x + 1       = 15x²       - 8x + 1

4x² + 4x + 1 - 15x² + 8x - 1
4x² - 15x² + 4x + 8x + 1 - 1
       -11x²      + 12x + 0

11x² + 12x = 0
x(11x + 12) = 0
x₁ = 0
e
(11x + 12) = 0
11x + 12 = 0
11x = - 12
x₂ = - 12/11


o) (2x-3) ( x+4)     = (x+2) ( 5x -6)
 2x² + 8x - 3x - 12 = 5x² -6x + 10x - 12
2x² + 5x - 12        = 5x² + 4x - 12
2x² + 5x - 12 - 5x² - 4x + 12= 0
2x² - 5x² + 5x - 4x - 12 + 12= 0
     -3x²   + x            0 = 0
-3x² + x = 0
x(-3x + 1) = 0
x
₁ = 0
e
(-3x +1) = 0
-3x + 1 = 0
-3x = - 1
x = - 1/-3
x
= + 1/3