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2010-03-06T15:36:19+01:00
A)1/3x²=-2 /×3
x² = -6
x² + 6 = 0

a = 1 , b = 0 , c = 6
Δ = 0² - 4 × 1 × 6
Δ = 0 - 24
Δ = -24
Δ < 0 brak rozwiązań
Z = Ф

b) x²+2/2=4x+1 /×2
2x² + 2 = 8x + 2
2x² - 8x = 0 /:2
x² - 4x = 0
a= 1, b = -4, c = 0
Δ = (-4)² - 4 × 1 × 0
Δ = 16
Δ >0
√Δ = 4
x₁ = -b-√Δ / 2a = 4 - 4 / 2×1 = 0/2 = 0
x₂ = -b+√Δ / 2a = 4 + 4 / 2 = 8/2 = 4
Z = {0,4}

c) x²-2=3x²-6
x² - 3x² -2 + 6 = 0
-2x² + 4 = 0 /: (-2)
x² - 2 = 0
a = 1 , b = 0, c= -2
Δ = 0² - 4 × 1 × (-2)
Δ = 8
Δ > 0
√Δ = 2√2
x₁ = -b-√Δ / 2a = 0 - 2√2 / 2 = -√2
x₂ = -b+√Δ / 2a = 0 + 2√2 / 2 = √2
Z= {-√2, √2}