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AstrumDigital
@AstrumDigital
July 2022
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x^4+5(x-2)^2+6x^2(x-2)=0 (однородное)
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kalbim
Verified answer
X^4 + 5*(x^2 - 4x + 4) + 6x^3 - 12x^2 = 0
x^4 + 6x^3 - 7x^2 - 20x + 20 = 0
x^2 * (x^2 + 6x - 7) - 20*(x - 1) = 0
x^2 * (x + 7)(x - 1) - 20*(x - 1) = 0
(x - 1)*(x^3 + 7x^2 - 20) = 0
x = 1
x^3 + 7x^2 - 20 = 0
Подбираем корень через делители свободного члена: +-1, +-2, +-4, +-5, +-10, +-20
x = -2 - корень уравнения, делим многочлен на многочлен:
(x^3 + 7x^2 - 20) / (x + 2) = x^2 + 5x - 10
x^2 + 5x - 10 = 0, D = 25 + 40 = 65
x = (-5 + √65) / 2
x = (-5 - √65) / 2
Ответ: 1, -2, (-5 + √65) / 2, (-5 - √65) / 2
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Answers & Comments
Verified answer
X^4 + 5*(x^2 - 4x + 4) + 6x^3 - 12x^2 = 0x^4 + 6x^3 - 7x^2 - 20x + 20 = 0
x^2 * (x^2 + 6x - 7) - 20*(x - 1) = 0
x^2 * (x + 7)(x - 1) - 20*(x - 1) = 0
(x - 1)*(x^3 + 7x^2 - 20) = 0
x = 1
x^3 + 7x^2 - 20 = 0
Подбираем корень через делители свободного члена: +-1, +-2, +-4, +-5, +-10, +-20
x = -2 - корень уравнения, делим многочлен на многочлен:
(x^3 + 7x^2 - 20) / (x + 2) = x^2 + 5x - 10
x^2 + 5x - 10 = 0, D = 25 + 40 = 65
x = (-5 + √65) / 2
x = (-5 - √65) / 2
Ответ: 1, -2, (-5 + √65) / 2, (-5 - √65) / 2