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x^2 - 5x + 2x - 10 =< 2|-2
x^2 - 3x - 12 =< 0
delta = 9 + 48 = 57
pier z delty = pier 57
x1 = 3 - pier 57/2
x2 = 3 + pier 57/2
(wykres - parabola ramionami do gory)
x nalezy do <x1;x2>
2. (3x-6)(x+2)>(x-1)(x+3)
3x^2 + 6x - 6x - 12>x^2 + 3x -x -3
2x^2 - 2x - 9>0
delta = 4 + 72 = 78
pier z delty = pier 78
x1 = 2-pier 78/4
x2 = 2+pier 78/4
(wykres - parabola ramionami do góry)
x nalezy do (x1;x2)
3. (x+2)² -1< lub równe 2(x-3)²
x^2 + 4x + 4 -1 =< 2(x^2 - 6x + 9)
x^2 + 4x + 3 =< 2x^2 - 12x + 18
-x^2 + 16x - 15 =<0
delta = 256 - 60 = 196
pier z delty = 14
x1 = -16 - 14/2 = -30/2 = -15
x2 = -16 + 14/2 = -2/2 = -1
(wyres - parabola ramionami w doł)
x nalezy do (-nieskończoności; x1> suma <x2; + nieskonczonosci)
x²-5x+2x-10≤2
x²-3x-10-2≤0
x²-3x-12≤0
Δ=9-4×1×(-12)
Δ=9+48
Δ=57
√Δ=√57
x₁=-b-√Δ/2a
x1=3-√57/2
x₂=-b+√Δ/2a
x₂=3+√57/2
x∈<3-√57/2;3+√57/2>
2. (3x-6)(x+2)>(x-1)(x+3)
3x²+6x-6x-12>x²+3x-x-3
3x²-12>x²+2x-3
3x²-12-x²-2x+3>0
2x²-2x-9>0
Δ=4-4×2×(-9)
Δ=4+72
Δ=76
√Δ=2√19
x₁=2-2√19/4=2(1-√19)/4=(1-√19)/2
x₂=2+2√19/4=(1+√19)/2
x∈(1-√19/2;1+√19/2)
3. (x+2)² -1≤2(x-3)²
x²+4x+4-1≤2(x²-6x+9)
x²+4x+3≤2x²-12x+18
x²+4x+3-2x²+12x-18≤0
-x²+16x-15
Δ=256-4×(-1)×(-15)
Δ=256-60
Δ=196
√Δ=14
x₁=-16-14/(-2)
x₁=15
x₂=-16+14/(-2)
x₂=1
x∈(-∞,1> u <15,+∞)