Rozwiąż równania:
x² - √2x - 4 = 0
6x² = x + 1
1.
a = 1, b = -√2, c = -4
Δ = b² - 4ac = (-√2)² - 4*1*(-4) = 2 + 16 = 18
√Δ = √18 = √(9*2) = 3√2
x₁ = (-b-√Δ)/2a = (√2 - 3√2)/2 = -√2
x₂ = (-b+√Δ)/2a = (√2 + 3√2)/2 = 2√2
x ∈ {-√2; 2√2}
2.
6x² - x - 1 = 0
Δ = b² - 4ac = (-1)² - 4*6*(-1) = 1 + 24 = 25
√Δ = 5
x₁ = (-b-√Δ/2a = (1-5)/12 = -1/3
x₂ = (-b+√Δ/2a = (1+5)/12 = 1/2
x ∈ {-⅓; ½}
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