a) [latex][(a+b)-c]^2 = a^2 + b^2 +c^2 +2ab[/latex] [latex](a+b)^2-2(a+b)c+c^2 =(a+b)^2 +c^2[/latex] [latex]-2(a+b)c =0 /:(-2c)[/latex] [latex]a+b=0[/latex] [latex]a=-b[/latex] ===================== b) [latex](a-b+c)^2 = a^2 + c^2 - 2ab +2ac[/latex] [latex][(a+c)-b]^2 = (a+c)^2- 2ab[/latex] [latex](a+c)^2-2(a+c)b+b^2= (a+c)^2- 2ab[/latex] [latex]-2(a+c)b+b^2=-2ab[/latex] [latex]-2ab-2cb+b^2=-2ab[/latex] [latex]-2cb+b^2=0[/latex] [latex]b(-2c+b)=0[/latex] [latex]b=0 lub -2c+b=0[/latex] [latex]. b=2c[/latex]
Wykaż,że: a)jeśli [latex]c eq 0 i (a+b-c)^{2}=a^{2}+b^{2}+c^{2}+2ab, to a=-b\b) jeśli b eq 0 i (a-b+c)^{2}=a^{2}+c^{2}-2ab+2ac, to b=2c[/latex]...
