Question

resolva as equações a)x2 -9x+9 = 0
b) 2x2 + 9=x2 -6x c)6x2+x-1=0 d)-16x+8-1=0 e) -9x2+6x-5=0
f)x2+3x-4=0

Answer 1

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

Δ = b² - 4ac
Δ = (-9)²  -4.1.9
Δ = 81 - 36
Δ = 45
√Δ = √9.√5
√Δ = 3√5

x = - b +/- √Δ = - ( - 9) +/- √45
          2a                2.1

x = 9 + 3√5
         2

x = 9 - 3√5
         2
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b)
2x² + 9 = x² - 6x
2x² - x² + 6x + 9 = 0
x² + 6x + 9 = 0
a = 1; b = 6; c = 9

Δ = b²  -4ac
Δ = 6²  -4.1.9
Δ = 36 - 36
Δ = 0

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

x = - 6
        2

x = - 3
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c)
6x² + x - 1 = 0
a = 6; b = 1; c = - 1

Δ = b²  -4ac
Δ = 1² - 4.6.(-1)
Δ = 1 + 24
Δ = 25

x = - b +/- √Δ = - 1 +/- √25
          2a              2.6

x = - 1 + 5  =  4  (:4)   =   1
          12       12  (:4)       3

x = - 1 - 5 = - 6  (:6)  =   - 1
        12       12   (:6)        2

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d)
- 16x² + 8x - 1 = 0

a = - 16; b = 8; c = - 1

Δ = b² - 4ac
Δ = 8²  -4.(-16).(-1)
Δ = 64 + 64.(-1)
Δ = 64 - 64
Δ = 0

x = - b +/- √Δ = - 8 +/- 0
          2a             2.(-16)

x =  - 8  =    8   (:8)   =   1
      - 32      32   (:8)       4
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e)
- 9x² + 6x - 5 = 0

a = - 9; b = 6; c = - 5

Δ = b² - 4ac
Δ = 6² - 4.(-9).(-5)
Δ = 36 + 36.(-5)
Δ = 36 -180
Δ = - 144 (não há solução para os Números Reais)
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f)
x² + 3x - 4 = 0

a = 1; b = 3; c = - 4

Δ = b²  -4ac
Δ = 3²  -4.1.(-4)
Δ = 9 + 16
Δ = 25

x = - b +/- √Δ = - 3 +/- √25
          2a                2.1

x = - 3 + 5  = 2/2 = 1
           2

x = - 3 - 5 = - 8/2 =  - 4
          2