a, b, c - ciąg arytmetyczny Mogę zatem zapisać, że: b = a + r c = a + 2r [latex]a+b+c=24[/latex] [latex]a+a+r+a+2r=24[/latex] [latex]3a+3r=24[/latex] [latex]3(a+r)=24[/latex] [latex]a+r=8[/latex] [latex]r=8-a[/latex] [latex]abc=120[/latex] [latex]a(a+r)(a+2r)=120[/latex] [latex]a(a+8-a)(a+16-2a)=120[/latex] [latex]8a(16-a)=120[/latex] [latex]128a-8 a^{2} =120[/latex] [latex]8 a^{2} -128a+120=0[/latex] [latex] a^{2} -16a+15=0[/latex] [latex](a-1)(a-15)=0[/latex] [latex]a=1[/latex] LUB [latex]a=15[/latex] DLA a=1: r = 8 - 1 = 7 a = 1 b = 1 + 7 = 8 c = 1 + 2*7 = 1 + 14 = 15 DLA a=15: r = 8 - 15 = - 7 a = 15 b = 15 - 7 = 8 c = 15 - 2*7 = 15 - 14 = 1
