rozwiąż równania : a) (x+1)^2=(2x-1)(x+1) b) (x-3)^2-2=(x-1)(2x-1) c) (x-1)(x+1)-3x^2+5x=0 d) 4x^2=(1-x)^2 e) -2x^2+5x-3=0 f) 5x^2=8x+5 g) -3x^2+2x-3=0

a) (x+1)^2=(2x-1)(x+1) x^2+2x+1=2x^2+2x-x-1 x^2+2x+1=2x^2+x-1 x^2-2x^2+2x-x+1+1=0 -x^2+x+2=0 del=b^2-4*a*c del=1-4*(-1)*2 del=1+8=9 pierw(del)=3 x1= (-b-pierw(del))/2a = (-1-3)/(-2)= (-4)/(-2)=2 x2= (-b+pierw(del))/2a = (-1+3)/(-2)= 2/(-2)=-1 b) (x-3)^2-2=(x-1)(2x-1) x^2-6x+9-2=2x^2-x-2x+1 x^2-6x+7=2x^2-3x+1 x^2-2x^2-6x+3x+7-1=0 -x^2-3x+6=0 del=(-3)^2-4*(-1)*6 del=9+24=33 pierw(del)=pierw(33) x1= (-b-pierw(del))/2a = (3-pierw(33))/(-2) x2= (-b+pierw(del))/2a = (3+pierw(33))/(-2) c) (x-1)(x+1)-3x^2+5x=0 x^2-1-3x^2+5x=0 -2x^2+5x-1=0 del= 25-4*(-2)*(-1) del=25-8=17 pierw(del)=pierw(17) x1= (-b-pierw(del))/2a = (-5-pierw(17))/(-4) x2= (-b+pierw(del))/2a = (-5+pierw(17))/(-4) d) 4x^2=(1-x)^2 4x^2=1-2x+x^2 3x^2+2x-1=0 del=4-4*3*(-1)=4+12=16 pier(del)=4 x1= (-b-pierw(del))/2a = (-2-4)/(6)=-6/6=-1 x2= (-b+pierw(del))/2a = (-2+4)/(6)=2/6=1/3 e) -2x^2+5x-3=0 del=25-4*(-2)*(-3) del=25-24=1 pierw(del)=1 x1= (-b-pierw(del))/2a = (-5-1))/(-4)=-6/(-4)=3/2 x2= (-b+pierw(del))/2a = (-5+1)/(-4)=-4/(-4)=1 f) 5x^2=8x+5 5x^2-8x-5=0 del=64-4*5*(-5) del=64+100=164 pierw(del)=2pierw(41) x1= (-b-pierw(del))/2a = (8-2pierw(41))/10= (4-pierw(41))/5 x2= (-b+pierw(del))/2a = (8+2pierw(41))/10= (4+pierw(41))/5 g) -3x^2+2x-3=0 del=4-4*(-3)*(-3) del=4-36=-32 Δ < 0, to równanie nie ma rozwiązań rzeczywistych.