Question

Calcule as razões das equações (U=R).

3x²=15x

(2x-1)²=0

x²-3x-10=0

x²-3x-10=0

x²+9=6x

5x+1=4(x+1)+x

5x²+7x+1=3x²+2x+1

2x+1=-(1-2x)

Answer 1

a)

3x² = 15x
3x² - 15x = 0
x.(3x - 15) = 0
x = 0

3x - 15 = 0
3x = 15
x = 15/3
x = 5

R.: x = 0 e x = 5
¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
b)

(2x - 1)² = 0
4x² - 2.1.2x + 1 = 0
4x² - 4x + 1 = 0
a = 4; b = - 4; c = 1

Δ = b² - 4ac
Δ = (-4)² - 4.4.1
Δ = 16 - 16
Δ = 0

x = - b +/- √Δ   = - ( - 4) +/- √0
      ---------------   ------------------
          2a                   2.4

x =   4  (:4)        1
      ------       = -----
        8  (:4)         2

x = 1/2

**************************************
c) = d)
x² - 3x - 10 = 0
a = 1; b = - 3; c = - 10

Δ = b² - 4ac
Δ = (-3)² - 4.1.(-10)
Δ = 9 - 4.(-10)
Δ = 9 + 40
Δ = 49

x = - b +/- √Δ    = - ( - 3) +/- √49
      -------------      ---------------------- 
          2a                    2.1

x = 3 + 7
      ---------  = 10/2 = 5
          2

x = 3 - 7    = - 4/2 = - 2
      --------
         2

R.: x = 5 e x = - 2

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
e)
x² + 9 = 6x
x² - 6x + 9 = 0
a = 1; b = - 6; c = 9

Δ = b² - 4ac
Δ = (-6)² - 4.1.9
Δ = 36 - 36
Δ = 0

a = 1; b = - 6; c = 9

x = - b +/- √Δ      =  - ( - 6) +/- √0
      ---------------      ----------------------  = 6/2 = 3
             2a                      2.1

R.: x' = x" = 3

*******************************
f)
5x + 1 = 4(x + 1) + x
5x + 1 = 4x + 4 + x
5x + 1 = 4x + x + 4
5x + 1 = 5x + 4
5x - 5x = 4 - 1
0 = 3  (não existe)

¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨¨
g)
5x² + 7x + 1 = 3x² + 2x + 1
5x² - 3x² + 7x - 2x + 1 - 1 = 0
2x² + 5x = 0
x.(2x + 5) = 0
x = 0

2x + 5 = 0
2x = - 5
x = - 5/2

R.: x = 0 e x = - 5/2
*************************************
h)
2x + 1 = - (1 - 2x)
2x + 1 = - 1 + 2x
2x - 2x = - 1 - 1
0 = - 2 (não existe)