[latex]-x^3+2x^2-9x+18=0\ -x^2(x-2)-9(x-2)=0\ (x-2)(-x^2-9)=0\ x-2=0 vee -x^2-9=0\ x=2 vee x=o\ \ x=2\ \ \ \ b)\ (5x+1)^2+x=(2x+5)^2-12\ 25x^2+10x+1+x=4x^2+20x+25-12\ 21x^2-9x-12=0 setminus :3\ 7x^2-3x-4=0\ \ Delta=b^2-4ac=(-3)^2-4*7*(-4)=9+112=121\ \ x_{1}=frac{-b-sqrt{Delta}}{2a}=frac{3-11}{14}=-frac{8}{14}=-frac{4}{7}\ \x_{2}=frac{-b+sqrt{Delta}}{2a}=frac{3+11}{14}=frac{14}{14}=1[/latex]
a) -x do trzeciej+ 2x do kwadratu - 9x +18=0 -xkwadrat (x-2)-9(x-2)=0 (x-2)(-x kwadrat-9)=0 x2 xkwadrat=9 x=3 v x=-3 b) 5(x+1)kwadrat +x=(2x+5)kwadrat - 12 5(x kwadrat +2x+ 1)+x=( 4 x kwadrat + 20 x + 25)-12 5 x kwadrat +10 x +5 +x= 4 x kwadart + 20 x + 25-12 5x kwadrat + 10 x +5 +x - 4x - 20x -25 +12=0 xkwadrat - 9x -8 =0 delta= b kwadrat - 4ac delta=(- 9) kwadrat- 4*1* (-8) delta=81+ 32 delta=113 pierwiastek z delty= pierwoastek z 113 x1=-b- pierwiastek z delty/2a x1=-(-9)- pierwiastek z 113/ 2 x1=9- pierwiastek z 113/ 2 x2=-b+pierwiastek z 113/ 2a x2=9+pierwiastek z 113/ 2
