Question

a) 3(x-2)-3=2(x-2)(x+2)
b) x(x-1)+4(x-2)=5(x-2) (x-1)
c) 2(x-1)=3x(x-1)-2x(x-1)
d)(6x+5)(x-1)=3x+5
e)2(x-2)-(x-3)(x-2) = 2(x-3)
f) 2-2(x-1)(x+1)=x(x+1
g) x(x-1)-3x(x-2)=3
Preciso disto pronto até 08:40

Answer 1

A) 3(x-2)-3=2(x-2)(x+2)
3x - 6 - 3 = (2x - 4)(x+2)
3x - 9 = 2x² + 4x - 4x - 8
2x² - 3x + 9 - 8 = 0
2x² - 3x + 1 = 0

Δ = (-3)² - 4.2.1 = 9 - 8 = 1

x =[-(-3) +- √1]/2.2

x' = [3 + 1]/4 = 4/4 = 1
x" = [3 - 1]/4 = 2/4 = 1/2

b) x(x-1)+4(x-2)=5(x-2) (x-1)
x² - x + 4x - 8 = 5(x² - x - 2x + 2)
x² + 3x - 8 = 5x² - 15x + 10
5x² - x² - 15x - 3x + 10 + 8 = 0
4x² - 18x + 18 = 0

Δ = 18² - 4.4.18 = 324 - 288 = 36

x = [-(-18) +- √36]/2.4 

x' = [18 + 6]/8 = 24/8 = 3

x" = [18 - 6]/8 = 12/8 = 3/2

c) 2(x-1)=3x(x-1)-2x(x-1)
2x - 2 = 3x² - 3x - 2x² + 2x
3x² - 2x² - 3x + 2x - 2x + 2 = 0
x² - 3x + 2 = 0

Δ = (-3)² - 4.1.2 = 9 - 8 = 1

x = [-(-3) +- √1]/2.1

x' = [3 + 1]/2 = 4/2

x" = [3 - 1]/2 = 2/2 = 1

d)(6x+5)(x-1)=3x+5
6x² - 6x + 5x - 5 = 3x + 5
6x² -x - 3x - 5 - 5 = 0
6x² - 4x - 10 = 0

Δ = (-4)² - 4.6.(-10) = 16 + 240 = 256

x = [-(-4) +- √256]/2.6

x' = [4 + 16]/12 =20/12 = 5/3

x" = [4 - 16]/12 = -12/12 = -1

e)2(x-2)-(x-3)(x-2) = 2(x-3)
2x - 4 -(x² - 2x - 3x + 6) = 2x - 6
2x - 4 - x² + 2x + 3x - 6 = 2x - 6
-x² + 2x + 2x + 3x- 2x  - 4 - 6 + 6 = 0
-x² + 5x - 4 = 0

Δ = 5² - 4.(-1).(-4) = 25 - 16 = 9

x = [-5 +- √9]/2.(-1)

x' = [-5 + 3]/-2 = -2/-2 = 1

x" = [-5 - 3]/-2 = -8/-2 = 4

f) 2-2(x-1)(x+1)=x(x+1)
2 - 2(x² + x - x - 1) = x² + x
2 -2x² + 2 = x² + x
-2x² - x² - x + 4 = 0
-3x² - x + 4 = 0 (x-1)
3x² + x - 4 = 0

Δ = [1² - 4.(3)(-4)] = 1 + 48 = 49

x = [-1 +- √49]/2.3 = [-1 +- 7]/6

x' = [-1 + 7]/6 = 6/6 =1

x" = [-1 - 7]/6 = -8/6 = -4/3

g) x(x-1)-3x(x-2)=3
x² - x - 3x² + 6 = 3
-2x² - x + 6 - 3 = 0
-2x² - x + 3 = 0
2x² + x - 3 = 0

Δ = 1² - 4.2.(-3) = 1 + 24 = 25

x = [-1 +-√25]/2.2

x' = [-1 + 5]/4 = 4/4 = 1

x" = [-1 - 5]/4 = -6/4 = -3/2

Espero ter ajudado.