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Vadik7809
@Vadik7809
July 2022
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Представьте произвидение в виде многочлена:
(1-x^2)(1+x^2+x^4)
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3c3uuj3v4g
1) M^3 - N^3 + 2N - 2M = (M-N)*(M^2 +MN + N^2) + 2*(N - M) = (M-N)*(M^2+MN+N^2+2)
2) X^4 +XY^3 -X^3*Y - Y^4 = (X^4 - X^3Y) + (XY^3 - Y^4) = X^3*(X - 1) + Y^3*(X - 1) =
= (X-1)*(X^3 + Y^3)
3) 5X*(X-3)^2 - 5*(X-1)^3 + 15*(X+2)*(X-2) = 5
5X*(X^2-6X+9)- 5*(X-1)*(X^2+ X + 1) +15*(X^2 - 4) = 5
5X^3 - 30X^2 + 45X -5X^3 + 5 + 15X^2 - 60 = 5
15X^2 + 45X - 60 = 0
15*(X^2 + 3X - 4)= 0
D = 9-4*1*(-4) = 25
V D = 5
X1 = (- 3 + 5 )\ 2 = + 1
X2 = - 8 \ 2 = - 4
ОТВЕТ: 1 и минус 4
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Answers & Comments
2) X^4 +XY^3 -X^3*Y - Y^4 = (X^4 - X^3Y) + (XY^3 - Y^4) = X^3*(X - 1) + Y^3*(X - 1) =
= (X-1)*(X^3 + Y^3)
3) 5X*(X-3)^2 - 5*(X-1)^3 + 15*(X+2)*(X-2) = 5
5X*(X^2-6X+9)- 5*(X-1)*(X^2+ X + 1) +15*(X^2 - 4) = 5
5X^3 - 30X^2 + 45X -5X^3 + 5 + 15X^2 - 60 = 5
15X^2 + 45X - 60 = 0
15*(X^2 + 3X - 4)= 0
D = 9-4*1*(-4) = 25
V D = 5
X1 = (- 3 + 5 )\ 2 = + 1
X2 = - 8 \ 2 = - 4
ОТВЕТ: 1 и минус 4