Matemáticas

1 .x2+15x+56=0 2. 2x2-6x+4=0 3.. x2+8x+16=0 4. 3x2-14x+8=0 Desarrollo


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lupealucian

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1)X² + 15X + 56 = 0 Donde: a = 1; b = 15; c = 56 [latex]X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/latex] [latex]X=\frac{-15\pm \sqrt{15^2-4(1)(56)}}{2(1)}[/latex]  [latex]X=\frac{-15\pm \sqrt{225-224}}{2}[/latex] [latex]X=\frac{-15\pm \sqrt{1}}{2}[/latex] [latex]X=\frac{-15\pm \ 1}{2}[/latex] X1 = [-15 + 1]/2 = -14/2 = -7 X2 = [-15 - 1]/2 = -16/2 = -8 X1 = -7;  X2 = -8 2) 2X² - 6X + 4 = 0 (simplifico entre 2) X² - 3X + 2 = 0 Donde: a =1; b = -3 c = 2 [latex]X=\frac{-(-3)\pm \sqrt{(-3)^2-4(1)(2)}}{2(1)}[/latex] [latex]X=\frac{3\pm \sqrt{9-8}}{2}[/latex] [latex]X=\frac{3\pm \sqrt{1}}{2}[/latex] [latex]X=\frac{3\pm \ 1}{2}[/latex] X1 = [3 + 1]/2 = 4/2 = 2 X2 = [3 - 1]/2 = 2/2 = 1 X1 = 2; X2 = 1 3) X² + 8X + 16 = 0 Donde: a = 1; b = 8; c = 16 [latex]X=\frac{-8\pm \sqrt{8^2-4(1)(16)}}{2(1)}[/latex] [latex]X=\frac{-8\pm \sqrt{64-64}}{2}[/latex]  [latex]X=\frac{-8\pm \sqrt{0}}{2}[/latex] X = -8/2 = -4 X = -4 4) 3X² - 14X + 8 = 0 Donde: a = 3; b = -14; c = 8 [latex]X=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/latex] [latex]X=\frac{-(-14)\pm \sqrt{(-14)^2-4(3)(8)}}{2(3)}[/latex] [latex]X=\frac{14\pm \sqrt{196-96}}{6}[/latex] [latex]X=\frac{14\pm \sqrt{100}}{6}[/latex] [latex]X=\frac{14\pm \ 10}{6}[/latex] X1 = [14 + 10]/6 = 24/6 = 4 X2 = [14 - 10]/6 = 4/6 = 2/3 X1 = 4; X2 = 2/3

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