Question

please solve it. .............

(22x+34y+55xy)×(34x+12y+87xy)​

Answer 1

Answer:

Step-by-step explanation:

x (x (y (4785 y + 3784) + 748) + y (3618 y + 1420)) + 408 y^2

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748 x^2 + y ((x (4785 x + 3618) + 408) y + x (3784 x + 1420))

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(11 x (5 y + 2) + 34 y) (x (87 y + 34) + 12 y)

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Expanded form:Step-by-step solution

4785 x^2 y^2 + 3784 x^2 y + 748 x^2 + 3618 x y^2 + 1420 x y + 408 y^2

Alternate form assuming x and y are positive:

11 x^2 (435 y^2 + 344 y + 68) + 2 x y (1809 y + 710) + 408 y^2

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Polynomial discriminant:

Δ_x = (12 y (55 y + 22) - 34 y (87 y + 34))^2

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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)((55 y x + 22 x + 34 y) (87 y x + 34 x + 12 y)) = 22 x (435 y^2 + 344 y + 68) + 2 y (1809 y + 710)

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d/(dy)((55 y x + 22 x + 34 y) (87 y x + 34 x + 12 y)) = 22 x^2 (435 y + 172) + 4 x (1809 y + 355) + 816 y

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Indefinite integral:Step-by-step solution

integral(22 x + 34 y + 55 x y) (34 x + 12 y + 87 x y) dx = 11/3 x^3 (5 y + 2) (87 y + 34) + x^2 y (1809 y + 710) + 408 x y^2 + constant

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Local minimum:More digits

min{(22 x + 34 y + 55 x y) (34 x + 12 y + 87 x y)}≈-24.2985 at (x, y)≈(2.35674, -0.343039)

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Definite integral over a square of edge length 2 L:

integral_(-L)^L integral_(-L)^L (22 x + 34 y + 55 x y) (34 x + 12 y + 87 x y) dy dx = 4/3 L^4 (1595 L^2 + 1156)