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Katy4579
@Katy4579
September 2021
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решите систему неравенств .
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janaro
1) 3x-3<2x+7; 3x-2x<7+3; x<10
-5x²+4x-24≤-4x²-5(цифра неразборчиво!!)x-4; 5x²-4x+24≥4x²+5x+4;
5x²-4x²-4x-5x+24-4≥0; x²-9x+20≥0
D=b²-4ac=9²-4*1*20=81-80=1
x=(-b+-√D)/2a х1=(9-1)/2=4 x2=(9+1)/2=5
(x-4)(x-5)≥0
x≤4
x≥5
ч∈(-∞;4]∪[5;+∞)
x∈(-∞;4]∪[5;10)
2) x²+8x+18>-3x-10; x²+8x+3x+18+10>0; x²+11x+28>0
D=11²-4*1*28=121-112=9
(-11-√9)/2=-14/2=-7
(-11+√9)/2=-8/2=-4
(x+7)(x+4)>0
x∈(-∞;-7)∪(-4;+∞)
x²-4x+2≤4-3x
x²-4x+3x+2-4≤0
x²-x-2≤0
1-4*1*(-2)=9
(1-3)/2=-1 (1+3)/2=2
(x+1)(x-2)≤0
x∈[-1;2]
x∈[-1;2]
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Answers & Comments
-5x²+4x-24≤-4x²-5(цифра неразборчиво!!)x-4; 5x²-4x+24≥4x²+5x+4;
5x²-4x²-4x-5x+24-4≥0; x²-9x+20≥0
D=b²-4ac=9²-4*1*20=81-80=1
x=(-b+-√D)/2a х1=(9-1)/2=4 x2=(9+1)/2=5
(x-4)(x-5)≥0
x≤4
x≥5
ч∈(-∞;4]∪[5;+∞)
x∈(-∞;4]∪[5;10)
2) x²+8x+18>-3x-10; x²+8x+3x+18+10>0; x²+11x+28>0
D=11²-4*1*28=121-112=9
(-11-√9)/2=-14/2=-7
(-11+√9)/2=-8/2=-4
(x+7)(x+4)>0
x∈(-∞;-7)∪(-4;+∞)
x²-4x+2≤4-3x
x²-4x+3x+2-4≤0
x²-x-2≤0
1-4*1*(-2)=9
(1-3)/2=-1 (1+3)/2=2
(x+1)(x-2)≤0
x∈[-1;2]
x∈[-1;2]