a)(3-x)(x+5)(2x-3)=0 3-x = 0 lub x+5 = 0 lub 2x - 3 = 0 x = 3 lub x = -5 lub x = 3/2 b)[latex]x^3-3x^2+4x-12=0[/latex] [latex]x^2(x-3)+4(x-3)=0[/latex] [latex](x^2+4)(x-3) = 0[/latex] [latex]x^2+4 = 0 lub x-3 = 0[/latex] [latex]x^2 = -4 sprzeczne lub x = 3[/latex] d). [latex]frac{2x+1}{x} + frac{4x} {2x+1} =5[/latex] zał. [latex]x eq 0 i x eq -frac{1}{2}[/latex] [latex](2x+1)^2 + 4x^2 = 5[/latex] [latex](2x+1)^2 + 4x^2 -5 = 0[/latex] [latex]4x^2 + 4x + 1 + 4x^2 - 5 = 0[/latex] [latex]8x^2 + 4x -4 = 0[/latex] [latex]Delta = 16 +4 cdot 8 cdot 4 = 144[/latex] [latex]sqrt Delta = 12[/latex] [latex]x_1 = frac{-4-12}{16} = -1[/latex] [latex]x_2 = frac{-4+12}{16} = frac{1}{2}[/latex] e). [latex]frac{2x^2-7x-29}{x^2-2x-15} =1 [/latex] zał.[latex]x^2-2x-15} eq 0[/latex] [latex]Delta = 4 + 60 = 64[/latex] [latex]sqrt Delta = 8[/latex] [latex]x_1 = frac{2-8}{2} eq -3[/latex] [latex]x_2 = frac{2+8}{2} eq 5[/latex] [latex]2x^2-7x-29 =x^2-2x-15[/latex] [latex]2x^2-7x-29 -x^2+2x+15=0[/latex] [latex]x^2-5x-14 =0[/latex] [latex]Delta = 25 + 56 = 81[/latex] [latex]sqrt Delta = 9[/latex] [latex]x_1 = frac{5-9}{2} = -2[/latex] [latex]x_2 = frac{5+9}{2} = 7[/latex]
