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2009-12-10T16:00:37+01:00

a) (x-3)(2x+5)≤ (2x-6)(2x-1)
2x²+5x-6x-15≤4x²-2x-12x+6
2x²-x-15≤4x²-14x+6
2x²-13x+21≥0
Δ=169-168=1
x₁=(13-1):4=3
x₂=(13+1):4=3,5
x∈(-∞,3>u<3,∞)

b) (2-8x)(x+1)>(1-4x)(x+2)
2x+2-8x²-8x>x+2-4x²-8x
-4x²+2x>0
2x(-2x+1)>0
2x=0 v -2x+1=0
x=0 v x=-1/2
x∈(-∞,1/2)u(0,∞)

c) (3-5x)(2x+1)<(2x+1)(3x+2)
6x+3-10x²-5x<6x²+4x+3x+2
-10x²+1x+3<6x²+7x+2
-16x²-6x+1<0
Δ=36+64=100
x₁=(6-10):(-32)=1/8
x₂=(6+10):(-32)=-1/2
x∈(-∞,-1/2)u(1/8,∞)

d) (2-6x)(3x+9)≥x²-9
6x+18-18x²-54x≥x²-9
-18x²-48x+18≥x²-9
-19x²-48x+27≥0
Δ=2304+2052=4356
√Δ=66
x₁=(48-66):(-38)=-18/38=-9/19
x₂=(48+66):(-38)=-3
x∈<-3,-9/19>
2009-12-10T17:49:46+01:00
A) (x-3)(2x+5)≤ (2x-6)(2x-1)
2x²-x-15≤4x²-14x+6
2x²-13x+21≥0
Δ=169-168=1
x₁=(13-1)/4=3
x₂=(13+1)/4=3,5
x∈(-∞,3>u<3,5;∞)

b) (2-8x)(x+1)>(1-4x)(x+2)
2x+2-8x²-8x>x+2-4x²-8x
-4x²+2x>0 /:2
-2x²+x>0
x(-2x+1)>0
2x=0 v -2x+1=0
x=0 v x=-1/2
x∈(-∞,1/2)u(0,∞)

c) (3-5x)(2x+1)<(2x+1)(3x+2)
-10x²+1x+3<6x²+7x+2
-16x²-6x+1<0
Δ=36+64=100
x₁=(6-10)/(-32)=1/8
x₂=(6+10)/(-32)=-1/2
x∈(-∞,-1/2)u(1/8,∞)

d) (2-6x)(3x+9)≥x²-9
-18x²-48x+18≥x²-9
-19x²-48x+27≥0
Δ=2304+2052=4356
√Δ=66
x₁=(48-66)/(-38)=-18/38=-9/19
x₂=(48+66)/(-38)=-3
x∈<-3,-9/19>

Pozdrawiam, Wiktor.
2009-12-10T18:52:40+01:00
(x-3)(2x+5)≤ (2x-6)(2x-1)
2x²-x-15≤4x²-14x+6
2x²-13x+21≥0
Δ=169-168=1
x₁=(13-1)/4=3
x₂=(13+1)/4=3,5
x∈(-∞,3>u<3,5;∞)
b) (2-8x)(x+1)>(1-4x)(x+2)
2x+2-8x²-8x>x+2-4x²-8x
-4x²+2x>0 /:2
-2x²+x>0
x(-2x+1)>0
2x=0 v -2x+1=0
x=0 v x=-1/2
x∈(-∞,1/2)u(0,∞)
c) (3-5x)(2x+1)<(2x+1)(3x+2)
-10x²+1x+3<6x²+7x+2
-16x²-6x+1<0
Δ=36+64=100
x₁=(6-10)/(-32)=1/8
x₂=(6+10)/(-32)=-1/2
x∈(-∞,-1/2)u(1/8,∞)
d) (2-6x)(3x+9)≥x²-9
-18x²-48x+18≥x²-9
-19x²-48x+27≥0
Δ=2304+2052=4356
√=66
x₁=(48-66)/(-38)=-18/38=-9/19
x₂=(48+66)/(-38)=-3
x∈<-3,-9/19>