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29
ПРИЛОЖЕНИЕ 5
ВАРИАНТЫ ЗАДАНИЙ ДЛЯ РЕШЕНИЯ СИСТЕМ УРАВНЕНИЙ
1. )0(
0
4
1
2
2
2
1
32
2
32
1
>
⎩
⎨
⎧
=+
=+
x
xx
xx
2.
)0(
0
4
1
2
2
2
1
32
2
32
1
<
⎩
⎨
⎧
=+
=+
x
xx
xx
3.
)0(
02
01
1
2
2
2
2
1
12
>
⎩
⎨
⎧
=−+
=+−
x
xxx
xx
4.
)0(
01
0cos
1
2
2
2
1
211
>
⎩
⎨
⎧
=−+
=−
x
xx
xxx
5.
)0(
01
0cos
1
2
2
2
1
211
<
⎩
⎨
⎧
=−+
=−
x
xx
xxx
6.
)0(
0
12
2
32
12
2
2
2
1
>
⎩
⎨
⎧
=−
=+
x
xx
xx
7.
)0(
0
12
2
32
12
2
2
2
1
<
⎩
⎨
⎧
=+
=+
x
xx
xx
8.
)0(
01
0sin
1
2
2
2
1
12
>
⎩
⎨
⎧
=−+
=−
x
xx
xx
9.
)0(
01
0sin
1
2
2
2
1
12
<
⎩
⎨
⎧
=−+
=−
x
xx
xx
10.
)0(
0
02
1
2
2
2
2
2
1
1
<
⎩
⎨
⎧
=−
=−+
−
x
ex
xxx
x
11.
)0(
0
02
1
2
2
2
2
2
1
1
>
⎩
⎨
⎧
=−
=−+
−
x
ex
xxx
x
12. )0(
01
0122
1
12
2
2
21
2
1
>
⎩
⎨
⎧
=+−
=+−+−
x
xx
xxxx
13.
)0(
0ln
02
2
12
1
2
2
2
1
>
⎩
⎨
⎧
=−
=−+
x
xx
xxx
14.
)0(
11
0122
1
12
2
2
21
2
1
>
⎩
⎨
⎧
−=+−
=++++
x
xx
xxxx
15.
)0(
02
1
2
1
2
2
2
1
32
2
32
1
>
⎩
⎨
⎧
=−+
=+
x
xxx
xx
16.
)0(
02
1
2
1
2
2
2
1
32
2
32
1
<
⎩
⎨
⎧
=−+
=+
x
xxx
xx
17.
)0(
01
0sin
1
2
2
2
1
211
>
⎩
⎨
⎧
=−+
=−
x
xx
xxx
18.
)0(
01
0sin
1
2
2
2
1
211
<
⎩
⎨
⎧
=−+
=−
x
xx
xxx
19.
)0(
01
0
1
1
2
2
2
1
2
2
1
1
>
⎪
⎩
⎪
⎨
⎧
=−+
=−
+
x
xx
x
x
x
20.
)0(
01
0
1
1
2
2
2
1
2
2
1
1
<
⎪
⎩
⎪
⎨
⎧
=−+
=−
+
x
xx
x
x
x
21.
)0(
0)1ln(
2
1
02
1
12
2
2
2
2
1
>
⎪
⎩
⎪
⎨
⎧
=+−
=−+
x
xx
xxx
22.
)0(
0)1ln(2
02
1
12
2
2
2
2
1
>
⎩
⎨
⎧
=+−
=−+
x
xx
xxx
23.
)0(
01
02
1
2
2
2
1
12
1
>
⎩
⎨
⎧
=−+
=−
−
x
xx
exx
x
29
ПРИЛОЖЕНИЕ 5
ВАРИАНТЫ ЗАДАНИЙ ДЛЯ РЕШЕНИЯ СИСТЕМ УРАВНЕНИЙ
⎧ x 2 3 + x22 3 = 4 ⎧ x 2 + x22 − 2 x1 = 0
1. ⎨ 12 ( x1 > 0) 13. ⎨ 1 ( x 2 > 0)
⎩ x2 − ln x1 = 0
2
⎩ x1 + x2 = 0
⎧ x 2 3 + x22 3 = 4 ⎧ x12 + 2 x1 + x22 + 2 x2 + 1 = 0
2. ⎨ 12 ( x1 < 0) 14. ⎨ ( x1 > 0)
2
⎩ x1 + x2 = 0 x
⎩ 2 − x1 + 1 = − 1
⎧ x − x1 + 1 = 0 ⎧ x12 3 + x22 3 = 1
3. ⎨ 22 ( x1 > 0) 15. ⎨ 2 2
( x 2 > 0)
⎩ x1 + x2 − 2 x1 = 0
2
x
⎩ 1 + x 2 − 2 x 2 = 0
⎧ x cos x1 − x2 = 0 ⎧ x12 3 + x22 3 = 1
4. ⎨ 12 2 ( x1 > 0) 16. ⎨ 2 2
( x2 < 0)
⎩ x1 + x2 − 1 = 0 ⎩ x1 + x2 − 2 x1 = 0
⎧ x cos x1 − x2 = 0 ⎧ x sin x1 − x2 = 0
5. ⎨ 12 2 ( x1 < 0) 17. ⎨ 12 2 ( x1 > 0)
⎩ x1 + x2 − 1 = 0 ⎩ x1 + x2 − 1 = 0
⎧ 2 x12 + x22 = 1 ⎧ x sin x1 − x2 = 0
6. ⎨ ( x 2 > 0) 18. ⎨ 12 2 ( x1 < 0)
⎩ x1 + x2 − 1 = 0
23
⎩ x2 − x1 = 0
⎧ 2x2 + x2 = 1 ⎧ x1
7. ⎨ 1 2 23 ( x 2 < 0) ⎪ − x2 = 0
19. ⎨ 1 + x12 ( x1 > 0)
⎩ x2 + x1 = 0
⎪ x2 + x2 − 1 = 0
⎩ 1 2
⎧ x − sin x1 = 0
8. ⎨ 22 ( x1 > 0)
2
⎩ x1 + x2 − 1 = 0 ⎧ x1
⎪ − x2 = 0
20. ⎨ 1 + x12 ( x1 < 0)
⎧ x − sin x1 = 0 ⎪ x2 + x2 − 1 = 0
9. ⎨ 22 ( x1 < 0) ⎩ 1 2
2
⎩ x1 + x2 − 1 = 0
⎧ x12 + x22 − 2 x2 = 0
⎪
⎧ x12 + x22 − 2 x2 = 0 21. ⎨ 1 ( x1 > 0)
10. ⎨ − x1
( x1 < 0) x
⎪⎩ 2 2− ln( x1 + 1) = 0
⎩ x2 − e = 0
⎧ x 2 + x22 − 2 x2 = 0 ⎧ x 2 + x22 − 2 x2 = 0
11. ⎨ 1 ( x1 > 0) 22. ⎨ 1 ( x1 > 0)
− x1 x
⎩ 2 − 2 ln( x + 1) = 0
⎩ x2 − e = 0 1
⎧ x 2 − 2 x1 + x22 − 2 x2 + 1 = 0 ⎧ x2 − 2 x1e − x1 = 0
12. ⎨ 1 ( x1 > 0) 23. ⎨ 2 2
( x1 > 0)
x
⎩ 2 − x1 + 1 = 0 ⎩ x1 + x2 − 1 = 0
