[latex]D) \(x+1)(x-1)- (x-1)(3-x) = 0 \ \x^{2}-1-(3x-x^{2}-3+x)=0\ \x^{2}-1-3x + x^{2}+3-x=0\ \2x^{2}-4x+2=0\ \Delta =b^{2}-4ac=(-4)^{2}-4cdot 2cdot 2=16-16=0[/latex] [latex]x_{0}=frac{-b}{2a}=frac{4}{2cdot 2}=frac{4}{4}=1[/latex] [latex]E)\x^{2} -(x-2)x =0 \ \x^{2}-x^{2}-2x=0\ \2x=0\ \x=0[/latex] [latex]F)\ (x-4)^{2} - (x-4)(2x-1)=0 \ \x^{2}-8x+16-(2x^{2}-x-8x+4)=0\ \x^{2}-8x+16-2x^{2}+x+8x-4=0\ \-x^{2}+x+12=0\ \Delta =b^{2}-4ac=1^{2}-4cdot (-1)cdot 12=1+48=49[/latex] [latex]sqrt{Delta }=sqrt{49}=7\ \x_{1}=frac{-b-sqrt{Delta }}{2a}=frac{-1-7}{2cdot (-1)}=frac{-8}{-2}=4\ \_{2}=frac{-b+sqrt{Delta }}{2a}=frac{-1+7}{2cdot (-1)}=frac{6}{-2}=-3[/latex] [latex]G)\ x(x-2)-3(x-2)x=0 \ \x^{2}-2x-3x^{2}+6x=0\ \-2x^{2}+4x=0[/latex] [latex]-2x(x-2)=0\ \-2x=0vee x-2=0\ \x=0vee x=2[/latex] [latex]H)\ 4x^{2} -9 =0 \ \(2x-3)(2x+3)=0\ \2x-3=0vee 2x+3=0\ \2x=3/:2vee 2x=-3/:2\ \x=frac{3}{2}vee x=-frac{3}{2}[/latex]
