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Gladanak
@Gladanak
August 2022
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решить уравнение (x-3)(x^2+2x+4)=x^2+5x-24
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AlbuRin
(x -3)(x^2 + 2x + 4) = x^2 + 5x - 24
x^2 + 5x - 24 = 0
По теореме Виета х_1 = -8, х_2 = 3
Тогда x^2 + 5x - 24 = (x + 8)(x - 3)
(x - 3)(x^2 + 2x + 4) - (x + 8)(x - 3) = 0
(x - 3)(x^2 + 2x + 4 - x - 8) = 0
1) x - 3 = 0 x_1 = 3
2) x^2 + x - 4 = 0
D = b^2 - 4ac = 1^2 - 4*1*(-4) = 1 + 16 = 17
x_2 = (-b + VD)/2a = (-1 + V17)/2
x_3 = 9-b - VD)/2a = (-1 - V17)/2
1 votes
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Gladanak
а теперь
Gladanak
в задании у меня ещё написано что надо найти произведение его решений
artalex74
произведение корней равно 3*(-4)=-12
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Answers & Comments
x^2 + 5x - 24 = 0
По теореме Виета х_1 = -8, х_2 = 3
Тогда x^2 + 5x - 24 = (x + 8)(x - 3)
(x - 3)(x^2 + 2x + 4) - (x + 8)(x - 3) = 0
(x - 3)(x^2 + 2x + 4 - x - 8) = 0
1) x - 3 = 0 x_1 = 3
2) x^2 + x - 4 = 0
D = b^2 - 4ac = 1^2 - 4*1*(-4) = 1 + 16 = 17
x_2 = (-b + VD)/2a = (-1 + V17)/2
x_3 = 9-b - VD)/2a = (-1 - V17)/2