Контрольная по ВМатем
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(1,0,1) |
(0,0,2) |
(1,1,1) |
(7,4,4) |
11 |
(2,3,1) |
(4,-4,-2) |
(1,0,0) |
(4,7,5) |
12 |
(1,-2,-5) |
(2,3,2) |
(-1,0,5) |
(-4,2,1) |
13 |
(1,2,-1) |
(2,3,-10) |
(0,4,1) |
(-2,6,7) |
14 |
(-1,2,0) |
(6,3,1) |
(-15,0,2) |
(0,5,7) |
15 |
(1,3,4) |
(0,1,2) |
(2,5,0) |
(1,-5,-7) |
16 |
(2,-3,5) |
(1,-2,12) |
(4,-1,7) |
(-3,0,9) |
17 |
(1,2,3) |
(2,4,1) |
(2,0,-3) |
(-2,7,9) |
18 |
(1,-1,1) |
(5,4,-2) |
(-1,2,2) |
(2,2,4) |
19 |
(3,-1,2) |
(4,-1,-1) |
(2,0,2) |
(5,9,4) |
20 |
(7,1,4) |
(9,-2,0) |
(0,3,-3) |
(0,1,2) |
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(3,1,4) |
(-3,-1,0) |
(2,1,-3) |
(7,3,2) |
22 |
(2,1,0) |
(3,-1,-4) |
(0,2,-2) |
(8,0,2) |
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(3,-1,-1) |
(3,1,4) |
(1,0,5) |
(4,6,1) |
24 |
(2,1,-1) |
(7,-1,3) |
(0,3,3) |
(5,2,1) |
25 |
(2,-3,7) |
(-3,-1,5) |
(9,0,1) |
(-1,0,1) |
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(7,-3,4) |
(3,2,-1) |
(4,1,1) |
(5,-2,0) |
27 |
(1,1,0) |
(2,1,-4) |
(0,1,0) |
(7,-1,-4) |
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(1,-1,4) |
(2,3,-4) |
(1,0,-5) |
(2,0,4) |
29 |
(2,-4,7) |
(8,1,0) |
(-1,-3,0) |
(-1,0,-4) |
30 |
(1,-1,0) |
(0,1,7) |
(-1,-2,-3) |
(4,3,1) |
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(-1,0,4) |
(-2,-1,1) |
(1,0,1) |
(1,2,-1) |
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(0,-2,1) |
(1,1,-1) |
(5,6,7) |
(1,-3,4) |
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(2,1,3) |
(0,-1,-1) |
(1,6,8) |
(1,2,-0.5) |
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(4,-1,-2) |
(4,0,3) |
(4,3,6) |
(1,2,3) |
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(0,6,1) |
(2,2,-2) |
(0,-3,6) |
(1,-1,-3) |
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(2,-1,0) |
(3,2,1) |
(-1,4,3) |
(1,1,4) |
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(1,1,0) |
(-1,2,7) |
(1,8,2) |
(2,1,-3) |
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(1,-1,-9) |
(0,-1,-4) |
(5,8,1) |
(2,3,-10) |
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(1,1,1) |
(6,9,3) |
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(1,1,1) |
(7,4,4) |
(1,0,1) |
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(4,-4,-2) |
(1,0,0) |
(4,7,5) |
(2,3,1) |
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(2,3,2) |
(-1,0,5) |
(-4,2,1) |
(1,-2,-5) |
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(2,3,-10) |
(0,4,1) |
(-2,6,7) |
(1,2,-1) |
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(-15,0,2) |
(0,5,7) |
(-1,2,0) |
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(4,6,1) |
(3,-1,-1) |
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(0,3,3) |
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(-1,0,5) |
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(1,3,4) |
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(-3,0,9) |
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(1,2,3) |
(-2,7,9) |
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(5,9,4) |
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(1,0,5) |
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(4,6,1) |
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(0,3,3) |
(2,1,-1) |
(5,2,1) |
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(-3,-1,5) |
(9,0,1) |
(2,-3,7) |
(-1,0,1) |
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(4,1,1) |
(7,-3,4) |
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(0,1,0) |
(1,1,0) |
(7,-1,-4) |
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(1,0,-5) |
(1,-1,4) |
(2,0,4) |
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(8,1,0) |
(-1,-3,0) |
(2,-4,7) |
(-1,0,-4) |
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(0,1,7) |
(-1,-2,-3) |
(1,-1,0) |
(4,3,1) |
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(-2,-1,1) |
(1,0,1) |
(1,2,-1) |
(-1,0,4) |
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(1,1,-1) |
(5,6,7) |
(1,-3,4) |
(0,-2,1) |
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(0,-1,-1) |
(1,6,8) |
(1,2,-0.5) |
(2,1,3) |
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(4,0,3) |
(4,3,6) |
(1,2,3) |
(4,-1,-2) |
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(2,2,-2) |
(0,-3,6) |
(1,-1,-3) |
(0,6,1) |
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(3,2,1) |
(-1,4,3) |
(1,1,4) |
(2,-1,0) |
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(-1,2,7) |
(1,8,2) |
(2,1,-3) |
(1,1,0) |
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(0,-1,-4) |
(5,8,1) |
(2,3,-10) |
(1,-1,-9) |
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(1,1,1) |
(6,9,3) |
(2,1,3) |
(0,0,2) |
Задача 8. Привести к каноническому виду данное уравнение кривой, используя теорию квадратичных формул и определить ее тип.
Вариант |
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Уравнение кривой |
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4x |
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+ 24xy +11y |
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− 20 = 0 |
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5x |
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4xy + 8 y |
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− 36 = 0 |
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6xy + 8 y |
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−12x − 26 y +11 = 0 |
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5x2 + 4 6xy + 7 y 2 − 22 = 0 |
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15x2 − 2 |
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55xy + 9 y 2 − 20 = 0 |
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5x2 + 23xy + 3 y 2 −12 = 0 24xy + 3y 2 − 36 = 0
5x2 + 8xy + 5 y2 − 9 = 0 4x2 + 24xy +11y 2 − 20 = 0
6x2 − 46xy + 5 y 2 − 26 = 0 13x2 + 48xy + 27 y 2 − 45 = 0 3x2 − 265xy − y2 − 8 = 0 x2 − 221xy + 5 y 2 − 24 = 0 17 x2 −16xy +17 y 2 − 250 = 0 3x2 + 10xy + 3 y2 − 8 = 0
9x2 + 24xy +16 y 2 +120x − 90 y = 0 5x2 + 6xy + 5 y 2 −16x −16 y −16 = 0 5x2 +12xy − 22x −12 y −19 = 0
4x2 + 4xy + y 2 − 2x −14 y + 7 = 0 x2 − xy − 2 y 2 + 3y −1 = 0
4x2 − 4xy + y 2 + 4x − 2 y + 1 = 0 x2 − 2xy + 5 y 2 + 2x + 14 y +13 = 0 x2 − 2xy − 3y 2 + 2x −18 y −19 = 0 x2 + 2xy + y 2 − 2x − 8 y + 7 = 0
5x2 − 26xy + 5 y 2 −10x + 26 y − 41 = 0 14x2 + 24xy + 21y2 − 4x +18 y −139 = 0 4xy + 3y 2 +16x + 12 y − 36 = 0
9x2 − 24xy + 16 y2 − 20x +110 y − 50 = 0 x2 − 6xy + y 2 −10x − 2 y −11 = 0
7x2 −10xy + 7 y2 − 4x + 4 y − 8 = 0 5x2 + 4xy + 2 y 2 = 18
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4x2 + 26xy + 3 y 2 = 24 6x2 + 25xy + 2 y 2 = 21 5x2 + 42xy + 3 y2 = 14 7x2 + 218xy + 4 y 2 = 15 3x2 + 214xy + 8 y 2 = 0 7x2 + 26xy + 2 y 2 = 24 9x2 + 42xy + 2 y 2 = 20 6x2 + 210xy + 3 y 2 = 16 4x2 + 43xy + 5 y 2 = 40 x2 + y2 − 4x + 6 y + 4 = 0
2x2 + 5 y 2 + 8x −10 y −17 = 0 x2 − 6 y 2 −12x + 36 y − 48 = 0 x2 − 8x + 2 y + 18 = 0
4x2 + 9 y2 + 32x − 54 y +109 = 0 6x2 − 465xy − 2 y 2 −16 = 0
2x2 + 3y 2 − 4x − 6 y = 10 10x2 + 8xy + 4 y 2 = 36
2x2 − 2xy − 4 y 2 + 6 y − 2 = 0 2x2 + 12xy − 5.5 y 2 −10 = 0 4x2 + 24xy +11y 2 − 20 = 0 5x2 + 4xy + 8 y 2 − 36 = 0
6xy + 8 y2 −12x − 26 y +11 = 0 5x2 + 46xy + 7 y 2 − 22 = 0 15x2 − 255xy + 9 y 2 − 20 = 0 5x2 + 23xy + 3 y 2 −12 = 0
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24xy + 3y 2 − 36 = 0 5x2 + 8xy + 5 y2 − 9 = 0
4x2 + 24xy +11y 2 − 20 = 0 6x2 − 46xy + 5 y 2 − 26 = 0 13x2 + 48xy + 27 y 2 − 45 = 0 3x2 − 265xy − y2 − 8 = 0 x2 − 221xy + 5 y 2 − 24 = 0 17 x2 −16xy +17 y 2 − 250 = 0 3x2 + 10xy + 3 y2 − 8 = 0
9x2 + 24xy +16 y 2 +120x − 90 y = 0 5x2 + 6xy + 5 y 2 −16x −16 y −16 = 0 5x2 +12xy − 22x −12 y −19 = 0
4x2 + 4xy + y 2 − 2x −14 y + 7 = 0 x2 − xy − 2 y 2 + 3y −1 = 0
4x2 − 4xy + y 2 + 4x − 2 y + 1 = 0 x2 − 2xy + 5 y 2 + 2x + 14 y +13 = 0 x2 − 2xy − 3y 2 + 2x −18 y −19 = 0 x2 + 2xy + y 2 − 2x − 8 y + 7 = 0
5x2 − 26xy + 5 y 2 −10x + 26 y − 41 = 0 14x2 + 24xy + 21y2 − 4x +18 y −139 = 0 4xy + 3y 2 +16x + 12 y − 36 = 0
9x2 − 24xy + 16 y2 − 20x +110 y − 50 = 0 x2 − 6xy + y 2 −10x − 2 y −11 = 0
7x2 −10xy + 7 y2 − 4x + 4 y − 8 = 0 5x2 + 4xy + 2 y 2 = 18
4x2 + 26xy + 3 y 2 = 24
76
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6x2 + 2 5xy + 2 y 2 = 21 |
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85 |
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5x2 + 4 2xy + 3 y2 = 14 |
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86 |
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7x2 + 2 18xy + 4 y 2 = 15 |
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87 |
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3x2 + 2 14xy + 8 y 2 = 0 |
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88 |
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7x2 + 2 6xy + 2 y 2 = 24 |
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9x2 + 4 2xy + 2 y 2 = 20 |
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90 |
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6x2 + 2 10xy + 3 y 2 = 16 |
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91 |
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4x2 + 4 3xy + 5 y 2 = 40 |
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92 |
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x |
2 |
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+ y |
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− 4x + 6 y + 4 = 0 |
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93 |
2x |
2 |
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5 y |
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+ 8x −10 y −17 = 0 |
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94 |
x |
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− 6 y |
2 |
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−12x + 36 y − 48 = 0 |
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95 |
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x |
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− 8x + 2 y + 18 = 0 |
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96 |
4x |
2 |
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+ 9 y |
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+ 32x − 54 y +109 = 0 |
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97 |
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6x2 − 4 65xy − 2 y 2 −16 = 0 |
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98 |
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2x |
2 |
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+ 3y |
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− 4x − 6 y = 10 |
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99 |
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10x |
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+ 8xy + 4 y |
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= 36 |
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100 |
2x |
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2xy − 4 y |
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+ 6 y − 2 = 0 |
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Задача 9. Методом параллельных сечений исследовать форму поверхности. Сделать рисунок.
Вариант |
Формула поверхности |
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x |
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+ 2 y |
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+ 4z |
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= 2 |
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2 |
2x |
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− 9 y |
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− z |
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= 36 |
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−2x2 + 3 y 2 + 4z 2 = 0 x2 − y 2 − 4z 2 = 0
−x2 + y 2 − z 2 = 1 2 y 2 + 2 = 2x
x2 + y 2 = 2
x2 − y 2 = 2 z 2 − y2 = 9 z 2 − x2 = 9 x2 + 2z 2 = 1 x2 − 2z 2 = 1 x2 − y 2 = 2
x2 − y = 0 x2 − z = 0 y 2 − z = 0 y2 − x = 1 z 2 − y = 1 z 2 + x = 1
x2 − 2 y2 + z 2 = 1 xy + x = 1
z 2 + 2x = 1 y2 + yz = 1
x2 − 2 y2 + z |
= 1 |
− x2 + y + z |
= 2 |
x2 + y2 − z 2 |
= 1 |
−x2 − y2 + z 2 = 1 x − y 2 − z 2 = 1 x2 − y 2 − z 2 = 1
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x2 − y − z 2 = 1 x2 − y 2 − z = 1 x2 + y 2 = 2
x2 − y 2 = 2 y2 + z 2 = x y 2 − z 2 = x x2 − z 2 = y x2 + z 2 = y x2 + z 2 = 1 y2 + z 2 = 1 2 y 2 − z 2 = 2 x2 − 4z 2 = 1 x2 − 2 y 2 = 1
x2 − z 2 = 0 y 2 − z 2 = 0
x2 + y 2 − z 2 = 9
−x2 + y 2 + z 2 = 1 x2 − y 2 + z 2 = 1
x2 + y 2 − z = 1 x2 + y = 1
y2 − z = 1
x2 + 2 y 2 + 4z 2 = 2 2x2 − 9 y 2 − z 2 = 36
−2x2 + 3 y 2 + 4z 2 = 0 x2 − y 2 − 4z 2 = 0
− x2 + y 2 − z 2 = 1
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56 |
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2 y |
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= 2x |
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57 |
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x |
2 |
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+ y |
2 |
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= 2 |
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58 |
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x |
2 |
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− y |
2 |
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= 2 |
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59 |
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z |
2 |
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− y |
2 |
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= 9 |
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60 |
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z |
2 |
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− x |
2 |
= 9 |
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61 |
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x |
2 |
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+ 2z |
2 |
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= 1 |
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62 |
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x |
2 |
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− 2z |
2 |
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= 1 |
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63 |
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x |
2 |
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− y |
2 |
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= 2 |
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64 |
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x |
2 |
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− y |
= 0 |
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65 |
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x |
2 |
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− z |
= 0 |
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66 |
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y |
2 |
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− z |
= 0 |
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67 |
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y |
2 |
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− x |
= 1 |
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68 |
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z |
2 |
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− y |
= 1 |
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69 |
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z |
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2 |
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+ x |
= 1 |
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70 |
x |
2 |
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− 2 y |
2 |
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+ z |
2 |
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= 1 |
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71 |
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xy + x = 1 |
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72 |
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z |
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2 |
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+ 2x = 1 |
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73 |
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y |
2 |
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+ yz = 1 |
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74 |
x |
2 |
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− 2 y |
2 |
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+ z |
2 |
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= 1 |
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75 |
− x |
2 |
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+ y |
2 |
|
+ z |
2 |
|
= 2 |
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76 |
x |
2 |
|
+ y |
2 |
− z |
2 |
= 1 |
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78 |
− x |
2 |
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− y |
2 |
|
+ z |
2 |
|
|
= 1 |
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79 |
|
x |
|
− y |
2 |
− z |
2 |
= 1 |
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80 |
x |
2 |
|
− y |
2 |
− z |
2 |
|
= 1 |
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81 |
|
x |
2 |
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− y − z |
2 |
= 1 |
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82 |
|
x |
2 |
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|
− y |
2 |
|
− z = 1 |
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83 |
|
|
|
|
x |
2 |
|
|
|
+ y |
2 |
|
= 2 |
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|
80