Question

Rozwiąż równania:

a). x^2+4x+4=1

b). x^2-6x+4=20

c). x^2+2x=3

Answer 1

a) x^2+4x+4=1

x²+4x+3=0

a=1

b=4

c=3

Δ=b²-4*a*c

Δ=4²-4*1*3

Δ=16-12

Δ=4

√Δ=2

 

x₁=-b-√Δ/2*a=-4-2/2*1=-6/2=-3

x₂=-b+√Δ/2*a=-4+2/2*1=-2/2=-1

 

b) x^2-6x+4=20

x²-6x-16=0

Δ=(-6)²-4*1*(-16)

Δ=36+64

Δ=100

√Δ=10

x₁=6-10/2=-4/2=-2

x₂=6+10/2=16/2=8

 

c) x^2+2x=3

x²+2x-3=0

Δ=2²-4*1*(-3)

Δ=4+12

Δ=16

√Δ=4

x₁=-2-4/2=-6/2=-3

x₂=-2+4/2=2/2=1

Answer 2

a)

x² + 4x + 4 = 1

x² + 4x + 3 = 0

Δ =16 -4*1*3 = 16 -12 = 4

√Δ = 2

x1 = [-4 -2]/2 = -6/2 = -3

x2 = [-4 +2]/2 = -2/2 = -1

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b)

x² - 6x + 4 = 20

x² -6x - 16 = 0

Δ = 36 -4*1*(-16) = 36 + 64 = 100

√Δ = 10

x1 = [6 - 10]/2 = -4/2 = -2

x2 = [6 + 10]/2 = 16/1 = 8

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c)

x² + 2x = 3

x² + 2x - 3 = 0

Δ = 4 -4*1*(-3) = 4 + 12 = 16

√Δ = √16 = 4

x1 = [-2 -4]/2 = -6/2 = -3

x2 = [-2 +4]/2 = 2/2 = 1

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