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>
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.
(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>
