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(x² - 3x)(x + 1) + 2x(x - 3) - 2x + 6 = 0
x(x - 3)(x + 1) + 2x(x - 3) - 2(x - 3) = 0
(x - 3)[x(x + 1) + 2x - 2] = 0
(x - 3)(x² + x + 2x - 2) = 0
(x - 3)(x² + 3x - 2) = 0
x - 3 = 0 ou x² + 3x - 2 = 0
*) x - 3 = 0
x = 3
*) x² + 3x - 2 = 0
Delta = 3² - 4*1*(-2) = 9 + 8 = 17
[tex]x_1=\dfrac{-3-\sqrt{17}}{2}\\\\x_2=\dfrac{-3+\sqrt{17}}{2}[/tex]
D'où : [tex]S=\{3;\dfrac{-3-\sqrt{17}}{2};\dfrac{-3+\sqrt{17}}{2}\}[/tex]
(x² - 3x)(x + 1) + 2x(x - 3) - 2x + 6 = 0
x(x - 3)(x + 1) + 2x(x - 3) - 2(x - 3) = 0
(x - 3)[x(x + 1) + 2x - 2] = 0
(x - 3)(x² + x + 2x - 2) = 0
(x - 3)(x² + 3x - 2) = 0
x - 3 = 0 ou x² + 3x - 2 = 0
*) x - 3 = 0
x = 3
*) x² + 3x - 2 = 0
Delta = 3² - 4*1*(-2) = 9 + 8 = 17
[tex]x_1=\dfrac{-3-\sqrt{17}}{2}\\\\x_2=\dfrac{-3+\sqrt{17}}{2}[/tex]
D'où : [tex]S=\{3;\dfrac{-3-\sqrt{17}}{2};\dfrac{-3+\sqrt{17}}{2}\}[/tex]