Решите уравнение: а) y^4-27y=0 d)x^3+7x^2=18x c)2x^4-5x^3-18x^2+45x=0 b)x^2-11x^2+28x=0 e)5x^4-6x^3+x^2=0

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вопрос

а) y^4 - 27y = 0
y(y^3 - 27) = 0
y(y - 3)(y^2 + 3y + 9) = 0
y = 0, y = 3, y = (-3 ± √(3^2 - 439)) / 2
y = 0, y = 3, y = (-3 ± √(-63)) / 2
y = 0, y = 3, y = (-3 ± 3√7i) / 2

b) x^2 - 11x + 28 = 0
(x - 4)(x - 7) = 0
x = 4, x = 7

c) 2x^4 - 5x^3 - 18x^2 + 45x = 0
x(2x^3 - 5x^2 - 18x + 45) = 0
x(x - 3)(2x^2 - 11x - 15) = 0
x(x - 3)(2x + 5)(x - 3) = 0
x = 0, x = 3, x = -5/2, x = 3

d) x^3 + 7x^2 - 18x = 0
x(x^2 + 7x - 18) = 0
x(x + 9)(x - 2) = 0
x = 0, x = -9, x = 2

e) 5x^4 - 6x^3 + x^2 = 0
x^2(5x^2 - 6x + 1) = 0
x^2(5x^2 - 5x - x + 1) = 0
x^2(5x(x - 1) - 1(x - 1)) = 0
x^2(x - 1)(5x - 1) = 0
x = 0, x = 1, x = 1/5