Question

1)x²+3=4x
2)x²=7x-12
3)-9x²=5-6x
4)13-2x-15x²=0
5)0=9-16x-4x²
6)x²+2x+x+2=0
7)2x²+4x-6=3x

Answer 1

a) x² + 3 = 4x
    x² + 3 - 4x = 0
    x² - 4x + 3 = 0

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

Δ = b² - 4ac
Δ = (-4)² - 4.1.3
Δ = 16 - 4.1.3
Δ = 16 - 12
Δ = 4

x = - b +/- √Δ
          2a

x = 4 +/-2
        2

x = 4 + 2 = 6/2 = 3
       2
x = 4 - 2 = 2/2 = 1
       2
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b) x² = 7x - 12
x² - 7x + 12 = 0
a = 1; b= - 7; c= 12

Δ = b² - 4ac
Δ = (-7)² - 4.1.12
Δ = 49 - 48
Δ = 1

x = 7 + 1 = 8/2 = 4
       2

x = 7 - 1 = 6/2 = 3
         2
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c) - 9x² = 5 - 6x
- 9x² - 5 + 6x = 0
- 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 Reais, pois Δ < 0)
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d) 13 - 2x - 15x² = 0
- 15x² - 2x + 13 = 0
a = - 15; b = - 2; c = 13

Δ = b² - 4ac
Δ = 4 - 4.(-15).13
Δ = 4 + 60.13
Δ = 4 + 780
Δ = 784

x = - b +/- √Δ = - (-2) +/- √784         
          2a               2.(-15)

x = 2 + 28 = 30/-30 = - 1
       - 30

x = 2 - 28 = - 26 = 26 (:2) = 13
        - 30     -30     30 (:2)   15
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e) 0 = 9 - 16x - 4x²
4x² + 16x - 9 = 0
a = 4; b = 16; c = - 9
Δ = b² - 4ac
Δ = 16² - 4.4.(-9)
Δ = 256 + 144
Δ = 400

x = - 16 +/- 20
            8
x = - 16 - 20 = - 36 (:4) = - 9
            8          8   (:4)      2

x = - 16 + 20 = 4 (:4)  = 1
           8          8  (:4)    2
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f) x² + 2x + x + 2 = 0
x² + 3x + 2 = 0
a = 1; b = 3; c = 2

Δ = b² - 4ac
Δ = 3² - 4.1.2
Δ = 9 - 8
Δ = 1

x = - 3 + / - 1
             2
x = - 3 - 1 = - 4/2 = - 2
         2
x = - 3 + 1 = - 2/2 = - 1
           2
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g) 2x² + 4x - 6 = 3x
2x² + 4x - 3x - 6 = 0
2x² + x - 6 = 0
a = 2; b = 1; c = - 6

Δ = b² - 4ac
Δ = 1 - 4.2.(-6)
Δ = 1 + 8.6
Δ = 1 + 48
Δ = 49

x = - 1 +/- 7
           4
x = - 1 - 7 = - 8/4 = - 2
          4
x = - 1 + 7 = 6/2 = 3
          2