др 6

5.1

x² + y² + z² = y  z  5

5.2

x cosz + z siny + tgz = 5

5.3

x²  y²  z² + 6z + 2x  4y = 0

5.4

x² + y² + z² = xy + 2

5.5

x tgy + z sinx = y lnz

x² + y² + z² = z  4

5.6

x² + y² + z²  2xz = 2

5.7

z³ + 3xy + 3y = 7z

cosz + z tg²y + y e^x = 6

5.8

x² + y² + z² = xyz + 4

5.9

x³ + y³ + z³ ­ 3xyz = 4

5.10

e^x + x + 2y + z² = 4z

5.11

x² + 2y² + 3z² = 59

5.12

x³ + 3xyz  z³ = 27

5.13

x + y ² + z³  x³y²z = 2

5.14

x² + y² + z²  2xy  2yz  2xz = 1

5.15

3x² + z ln5  ctgxz = lny + 1

5.16

5.17

5.18

x²  2y² + z² + 4x + 2z + 2 = 0;

5.19

x² + y² + z²  4z = 8

5.20

3x² + 2y²  z²  xz + y = 2

5.21

x + y + z + 2 = xyz

x cosy  z tgx + y ctgz = 0

5.22

x²  2xy  3y² + 6x + z²  8z = 20

x² + 2y² + z³ = e^3xyz

5.23

z³ + 3xyz + 3y = 7x

x cosz + z tg²y + y e^x = 6

5.24

5.25

xyz + x³ + y³ + z³ = 7 + sin²xyz

5.26

xzy² + 2z² + 3yz + 4 = 0

5.27

x²  2y² + 3z²  yz + y = 2

5.28

5.29

x³ + 2y³ + z³ = 3xyz + 2y + 15

5.30

6.1

z = arcsin(4y  3x)

6.2

z = arccos(4x y)

6.3

z = y ln(y²  x²)

z = arcsin(x  5y)

6.4

6.5

z = ln(y² + x²)

z = arctg(x + y)

z = tgxy²

6.6

z = arctg(5x + 2y)

z = 2x²y  x³y²

6.7

z = x + arcctg(y + 2x)

z = sin²(y  3x)

z = ctgx²y

6.8

z = arcsinxy

6.9

z = y² lnx

6.10

z = cos²(x + y)

z = ln(x² + y² + 2x  4)

6.11

z = x lnxy

6.12

z = arctg(2  3xy)

6.13

z = x tgy²

6.14

z = sin(3y²  x²)

6.15

z = ln(5xy  y²)

6.16

z = ln(x² + xy)

6.17

z = ln(x + y²)

z = e^xlny + lnx siny

6.18

6.19

z = arctg(2x  y)

z = x sinxy

6.20

z = ln(3x²  2y³)

z=y² tgx

6.21

6.22

z = ln(4x²  5y²)

z = xe^xsiny

z = arcctg(2x + 5y)

6.23

z = xy  3x²  2y² +10

z = arctg(2x²  y)

6.24

z = cos³(2x  y)

6.25

6.26

z = ln(x² + (y  5)²)

6.27

.

6.28

6.29

z = x² ln(y  4)

z = x arcctg(x + 2y)

6.30

z =e^x(siny + cosx)

z = (2x²y + y³)³

7.1

z = x³ + 8y³  6xy + 5

z = x² + 2y²  4xy  6x + 1

7.2

z = 2xy  5x²  3y² + 2

z = xy(12  x  y)

7.3

z = x²  xy + y² + 9x  6y + 20

7.4

z = 1 + 15x  2x²  xy  2y²

z = x³ + 8y²  6xy  10

7.5

z = 8x³  xy² + 6x² + y²

z = 2(x + y)  x²  y²

7.6

z = 2  5y²  3x² + 2xy

z = 8  3x + 27y + x²  y²

7.7

z = 2x³ + 2y³  6xy  5

z = e^3x(3x  2y²)

7.8

z = x³ + y³  6xy  20

7.9

z = 1 + 6x  x²  xy  y²

z = 3x³ + 3y³  9xy + 10

7.10

z = x² + xy + y²  6y  1

7.11

z = e^2x(x + y² + 2y)

z = xy  x²  y²  x  y

7.12

z = 4(x  y)  x²  y²

7.13

z = x²y  8y³  6y²  x²

z = x² + y²  2x  2y

7.14

z = x² + y² + x + y  xy

7.15

z = x² + y² + xy  3x  6y

z = (y  4)²  3x²

7.16

z = x² + 3(y + 2)²

7.17

z = (x  5)² + y² + 1

z = x² + 3y² + 4xy

7.18

z = 2xy  2x²  4y²

z = x³ + y³  3xy

7.19

z = x² + xy + y²  6x  1

z = x³ + y³  6xy  63x + 18y

7.20

z = 6(x  y)  3x²  3y²

z = x²  xy + y²  9x

7.21

z = x³ + y²  3x  6y

7.22

z = 2xy  3x²  2y² + 10

z = e^2y(2y  3x²)

7.23

z = 6xy  2x³  2y³  5

z = xy 3x² + 2y² + 10

7.24

z = x³ + 3xy²  15x + 12y

7.25

z = x³ + y²  6xy  39x + 18y + 20

z = (x  2)² + 2y²  10

7.26

z = x² + xy + y² + x  y + 1

7.27

z = x² + xy + y²  6x  9y

z = xy  x²  y² + 9

7.28

z = xy(x + y 12)

z = 6xy  x³  8y³  5

7.29

z = x² + y²  xy + x + y

z= xy(6  x  y)

7.30

z= 4(x  1)² + 5y² + 3

z = x² + xy + y²  2x  y

8.1

z = x² + 2xy + 4x  y²

D: x = 0, y = 0, x + y + 2 = 0

z = 3x²  x³ + 3y² + 4y

D : x = 0, x = 1, y = 0, y = 2

8.2

8.3

z = 4(y  x)  x²  y²;

D : x + 2y = 4, x  2y = 4, x = 0.

z = x³ + y³  3xy;

D : x = 0, y = 2, x = 2, y = 1.

8.4

z = xy  x  2y

D : x = 3, y = x, y = 0

z = x³ + 2xy  4x + 8y

D : x = 0, x = 1, y = 0, y = 2

8.5

z = 5x²  3xy + y²  4

D : x = 1, x = 1, y = 1, y =1

z = x² + 2xy  4x + 8y

D : y = x  1, x = 3, y = 0

8.6

8.7

z = x² + y³  2x  6y + 8

D : x = 0, y = 0, y = 1 x

z = 3xy  5x²  y² + 4

D : x = 1, y = 1, x = 1, y = 1

8.8

z = y² + 2xy  4y + 8x

D : y = 0, x = 3, x  y + 1 = 0

z = x³ + y²  3x + 2y

D : x = 0, y = 0, x = 2, y = 2

8.9

z = 3x + y  xy

D : y = x, y = 4, x = 0

z = x² + 2xy  10

D : y = 0, y = x²  4

8.10

z = 2xy + x²  y²  4x

D : x = 2, y = 0, y = x + 1

z = 4x  x²  2xy  8y

D : x = 0, x = 1, y = 0, y = 2

8.11

z = x² + 2xy  y²  2x + 2y

D : x = 2, y = 0, y = x + 2

z = 6xy  9x²  9y² + 4x + 4y

D : x = 0, x = 1, y = 0, y = 2

8.12

z = 2x²y  x³y  x²y² + x + y

D : x + y = 6, x = 0, y = 0

8.13

z = 3xy  x²  5y² + 4

D : x = 1, y = 1, x = 1, y = 1

z = 4y  y²  2xy  8x

D : x = 3, y  x + 1 = 0, y = 0

8.14

z = 2x³  xy² + y²

D : x = 0, x = 1, y = 0, y = 6

z = 2x + 2y  3x²  3y²  5

D : x = 0, y = 0 , x + y  1 = 0

8.15

z = 10  2x²  3y²

D : x = 2, x = 4, y = 0, y = 1

z = y (4  x  y)

D : x = 0, y = 0, y = 6  x.

8.16

z = 3y + x  xy

D : y = x, x = 4, y = 0

z = x²  y²  2xy  4y

D : x = 0, y = 0, x + y + 2 = 0

8.17

z = 3x² + 3y²  2x  2y + 2

D : x = 0, y = 0, x + y 1 = 0

8.18

z = x²  2xy  y² + 4x + 1

D : x = 3, y = 0, x + y + 1 = 0

8.19

z = 4y  y²  2xy  8x

D : x = 0, x = 1, y = 0, y = 2

z = 3x² + 3y²  x  y + 1

D : x = 5, y = 0, x  y  1 = 0

8.20

z = xy 2x  y

D : x = 0, x = 3, y = 0, y = 4

z = 10  y²  2xy

D : x = 0, x = y²  4

8.21

z = 5 + x + y  3x²  3y²

D : x = 2, y = 0, x  y + 1 = 0

z = 2xy  x² + y²  4x  10

D : x = 1, y = 0, x = 1, y = 2

8.22

z = x² + xy  2

D : y = 0, y = 4x²  4

z = xy  3x  2y

D : x = 0, x = 4, y = 0, y = 4

8.23

z = x² + y³  2x  3y + 8

D : x = 0, y = 0, x + y  3 = 0

z = 3x + 6y  x²  xy  y²

D : x = 0, y = 0, x = 1, y = 1

8.24

z = x²  2y² + 4xy  6x  1

D : x = 0, y = 0, x + y  1 = 0

8.25

z = 3x + y  xy

D : x = 1, x = 2, y = 0, y = 1

8.26

z = xy² (x  4 + y)

D : x = 0, y = 0, x + y = 6

8.27

z = x³ + y²  3x + 2y

D : x = 0, y = 2, x = 1, y = 4

z = 4(x  2)² + 2y²  3

D : x = 0, y = 0, x = 3 + y

8.28

z = x² + y² + xy  3x  6y

D : x = 1, x = 2, y = 1, y = 3

8.29

z = (y  4)²  3x²

D : x = 0, y = 0, x = 2, y = 5

8.30

z = 2(x + y)  x²  y²

D : x = 1, y = 1, x + y = 0

z = x³ + y²  3x  6y

D : x = 2, x = 3, y = 2, y = 3