Zad.1 w(x)=(x-√2)(x+√2)(x-1)(x+1) W(X)=(x²-2)(x²-1) w(x)=x⁴-x²-2x²+2 w(x)=x⁴-3x²+2 W(X)=x⁴+ax³+bx²+cx+d a=0, b= -3, c=0 , d=2 Zad.2 a) 4x³-4x²-15x=0 x(4x²-4x-15)=0 x=0 v 4x²-4x-15=0 Δ=16+240=256 √Δ=16 x₁=(4-16):8=-12/8=-3/2 x₂=(4+16):8=20/8=5/2 b)5x³+2x²-20x-8=0 x²(5x+2)-4(5x+2)=0 (5x+2)(x²-4)=0 (5x+2)=0 v (x²-4)=0 5x=-2 v (x+2)(x-2)=0 x=-2/5 v x=-2 v x=2 c)(-x²-6x+7)(1-x)≤0 Δ=36+28=64 , x=1 √Δ=8 x₁=(6-8):(-2)=1 x₂=(6+8):(-2)=-7 rysujemy wezyk od gory od prawej i odbija w x=1 mamy x∈(-∞,-7> u {1} d)x³-5x²-x+5≤0 x²(x-5)-(x-5)≤0 (x-5)(x²-1)≤0 (x-5)(x-1)(x+1)≤0 x=5 v x=1 v x=-1 wezyk od prawej od gory przebija miejsca zerowe x∈(-∞,-1>u<1,5> Zad.3 W(2)=4/(2-a) W(-3)=-1/(-3-a) 4/(2-a)=-1/(-3-a) zal. 2-a≠0 i -3-a≠0 a≠2 i a≠-3 D=R/{-3,2} (2-a)*(-1)=4*(-3-a) -2+a=-12-4a a+4a=-12+2 5a=-10 a=-2∈D Zad.4 zal. x+1≠0 i x-2≠0 x≠-1 i x≠2 D=R/{-1,2} (2x-3)/(x+1)-1=(x)/(x-2) [(2x-3)(x-2)-(x+1)(x-2)-x(x+1)]:[(x+1)(x-2)]=0/*(x+1)(x-2) (2x-3)(x-2)-(x+1)(x-2)-x(x+1)=0 2x²-4x-3x+6-(x²-2x+1x-2)-(x²+x)=0 2x²-7x+6-x²+x+2-x²-x=0 -7x=-8 x=8/7∈D Zad.5 (3/4;x;5/7+2x)-c.arytm x-3/4=5/7+2x-x x-3/4=x+5/7 0=5/7+3/4 nie istnieje taka liczba Zad.6 a₁=12 a₄=-6 a₁=12 a₁+3r=-6 a₁=12 12+3r=-6 a₁=12 3r=-18→r=-6 S₂₀=[2a₁+19r]*20:2 S₂₀=[2*12+19(-6)]*10=[24-114]*10=-900 Zad.7 (27,x,y)-c.geom x/27=y/x x²=27y (x,y,-3)-c.arytm y-x=-3-y 2y+3=x x²=27y 2y+3=x (2y+3)²=27y 2y+3=x 4y²+12y+9-27y=0 4y²-15y+9=0 Δ=225-144=81 √Δ=9 y₁=(15-9):8=6/8=3/4 y₂=(15+9):8=24:8=3 x=2*3/4+3=4,5 i y =3/4 lub x=2*3+3=9 i y=3 Zad.8 a) log√2:[2log4-log8]= =log√2:[log4²-log8]= =log√2:[log16-log8]= =log√2:[log2]= =1/2log2:log2=1/2 b) 27⁻²*9⁶=3⁻⁶*3¹²=3⁶=729
