Wzory skróconego mnożenia: [latex](a+b)^{2}=a^{2}+2ab+b^{2}\ (a-b)^{2}=a^{2}-2ab+b^{2}\ (a+b)(a-b)=a^{2}-b^{2}[/latex] ----------------------------------------------------------------------------------------------- [latex](x-1)(x+1)+x^{2}-1=2x^{2}-2\ x^{2}-1+x^{2}-1=2x^{2}-2\ 2x^{2}-2=2x^{2}-2\ 2x^{2}-2x^{2}=-2+2\ 0=0[/latex] Równanie oznaczone - równanie, które ma nieskończenie wiele rozwiązań. ----------------------------------------------------------------------------------------------- [latex](x-4)^{2}=(x-2)(x+2)\ x^{2}-8x+16=x^{2}-4\ x^{2}-x^{2}-8x=-4-16\ -8x=-20 |:(-8)\ x=frac{20}{8}\ x=frac{5}{2}\ x=2frac{1}{2}[/latex] ----------------------------------------------------------------------------------------------- [latex]x^{2}+(3x-3)(x+1)=1+(2x-1)^{2}\ x^{2}+3x^{2}-3x+3x-3=1+4x^{2}-4x+1\ 4x^{2}-3=4x^{2}-4x+2\ 4x^{2}-4x^{2}+4x=2+3\ 4x=5 |:4\ x=frac{5}{4}\ x=1frac{1}{4}[/latex]
