Question

Rozwiaz nierownosci : x^ <2-x , 4x^ wieksze badz rowne 4x-1 , x^ mniejsze badz równe 4.

Answer 1

x² < 2-x

x²+x-2 < 0

a = 1,  b = 1,  c = -2

Δ = b²-4ac = 1+8 = 9

√Δ = √9 = 3 

x1 = (-b-√Δ)/2a = (-1-3)/2 = -4/2 = -2

x2 = (-b+√Δ)/2a = (-1+3)/2 = 2/2 = 1

a > 0, ramiona paraboli skierowane w górę

D: x ∈ (-2;1)

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4x² ≥ 4x-1

4x²-4x+1 ≥ 0

a = 4,  b = -4,  c = 1

Δ = b²-4ac = 16-16 = 0

x = -b/2a = 4/8 = 1/2  

a = 4 > 0, ramiona paraboli skierowane w górę

D = R

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x² ≤ 4

x²-4 ≤ 0

(x+2)(x-2) ≤ 0

x = -2  v  x = 2

a = 1 > 0, ramiona paraboli skierowane w górę

D: x ∈(-∞; -2> u <2;+∞)