а) Не знаю, как ставить скобки в ворде, 35 лет назад решала такое, но решение точно развернутое.
X - 3Y = 6
2Y - 5X = 4
X = 3Y + 6
2Y = 5X +4
2Y = 5 (3Y+6) +4
2Y = 15Y + 30 +4
2Y - 15Y = 30 +4
-13Y = 34
Y = -34/13
X = 3 ( -34/13) + 6
X = -3/1 x 34/13 + 6
X = -102/13 + 6/1
X = -102/13 + 78/13
X = -24/13
Проверка:
X - 3Y = 6
-24/13 - 3 (- 34/13) = 6
-24/13 = 6
78/13 = 6
6 = 6
б)
Y = 5 -X
3X - Y = 11
Y = 5 -X
3X = 11 + Y
3X = 11 + (5 -X)
3X = 11 + 5 -X
3X = 16 -X
3X + X = 16
4X = 16
X = 4
Y = 5 - 4
Y = 1
Проверка
Y = 5 -X
1 = 5 - 4
1 = 1
в)
3X - 2Y = 5
11X +3Y = 39
3X = 5 + 2Y
3Y = 39 - 11X
X = (5 + 2Y) : 3
Y = (39 - 11X) : 3
X = 5/3 + 2/3 Y
Y = 39/3 - 11/3 X
X = 5/3 + 2/3 ( 39 - 11X)
X = 5/3 + 2/3 x 39/3 + 2/3 (- 11/3 X)
X = 5/3 + 78/9 - 22/9 X
X + 22/9 X = 5/3 +78/9
X + 22/9 X = 15/9 +78/9
31/9 X= 93/9
X= 93/9 : 31/9
X= 93/9 x 9/31
X= 3
Y = 39/3 - 11/3 X
Y = 39/3 - 33/3
Y = 6/3 = 2
Проверка
3X - 2Y = 5
3 x 3 - 2 x 2 = 5
9 - 4 = 5
5 = 5
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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