[latex]a)\ \7-(2+x)(2-x)=(x+1)^2 \ \7-(4-x^2)=x^2+2x+1\ \7-4+x^2-x^2-2x=1\ \-2x=1-3\ \-2x=-2/:(-2)\ \x=1[/latex] [latex]spr. \ \7-(2+1)(2-1)=(1+1)^2 \ \7-3=2^2\ \4=4\ \L=P[/latex] [latex]b)\ \ (x-10)(x+10)=(x-10)^2\ \(x-10)(x+10)-(x-10)^2=0\ \(x-10)(x+10 -(x-10))=0\ \(x-10)(x+10-x+10)=0[/latex] [latex]20(x-10)=0\ \x-10 =0\ \x=10 \ \spr.\ \(10-10)(10+10)=(10-10)^2[/latex] [latex]0*20=0^2\ \0=0\ \L=P[/latex]
Wzory skróconego mnożenia: (a+b)²=a²+2ab+b² - kwadrat sumy; (a-b)²=a²-2ab+b² - kwadrat różnicy; a²-b²=(a-b)(a+b) - różnica kwadratów. -------------------------------------------------------------- a) 7-(2+x)(2-x)=(x+1)² 7-(4-x²)=x²+2x+1 7-4+x=x²+2x+1 3-1=2x 2x=2 x=1 Sprawdzenie: 7-(2+1)(2-1)=(1+1)² 7-3*1=2² 7-3=4 4=3 L=P ---------------------------------------------- b) (x-10)(x+10)=(x-10)² x²-100=x²-20x+100 -20x=-200 x=10 Sprawdzenie: (10-10)(10+10)=(10-10)² 0*10=0² 0=0 L=P
