Разложите на множетели х^2 5х^3у 5ху^3 у^2

Question

Алгебра: Разложите на множетели х^2 5х^3у 5ху^3 у^2

Kykyshonochek1305 · Accepted Answer

y = -x^(3/2)/sqrt(2)

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y = x^(3/2)/sqrt(2)

Polynomial discriminant:

Δ_x = -108 y^4

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Integer roots:

x = 2, y = ± 2

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x = 8, y = ± 16

x = 18, y = ± 54

x = 0, y = 0

Properties as a function:Domain:

R^2

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Range:

R (all real numbers)

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Partial derivatives:Step-by-step solution

d/(dx)(2 y^2 - x^3) = -3 x^2

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d/(dy)(2 y^2 - x^3) = 4 y

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Indefinite integral:Step-by-step solution

integral(-x^3 + 2 y^2) dx = 2 x y^2 - x^4/4 + constant

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Definite integral over a disk of radius R:

integral integral_(x^2 + y^2<R^2)(2 y^2 - x^3) dx dy = (π R^4)/2

Definite integral over a square of edge length 2 L:

integral_(-L)^L integral_(-L)^L (-x^3 + 2 y^2) dy dx = (8 L^4)/3

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