# Sistemi di disequazioni di secondo grado

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```Sistemi di disequazioni di secondo grado
Algebra
1
2
3
4
5
6
7
8
9
10
11
v 3.0
1
(π₯π₯ β 2) + 2π₯π₯
4π₯π₯
β
1
>
οΏ½
3
π₯π₯ 2 β 3π₯π₯ + 2 > 0
1
< π₯π₯ < 1 β¨ π₯π₯ > 2
5
3π₯π₯ 2 β€ 4π₯π₯ + 7
οΏ½2π₯π₯ β 3 π₯π₯ π₯π₯ β 5
+ <
+3
5
2
2
β1 β€ π₯π₯ β€
βπ₯π₯(π₯π₯ + 2) > β2
5 β π₯π₯ 5
οΏ½π₯π₯
β€ π₯π₯ β
+
4
2
2
9
4
0 β€ π₯π₯ < β1 + β3
3π₯π₯ + 1 3
3
(1 + π₯π₯) β
π₯π₯(π₯π₯
β
4)
+
β₯
οΏ½
4
4
4
2
3π₯π₯ + 7π₯π₯ + 2 > 0
π₯π₯ < β2 β¨
1
4 β β15
β < π₯π₯ β€
3
2
4 + β15
β¨ π₯π₯ β₯
2
οΏ½
3 < π₯π₯ < β
(π₯π₯ + 3)2 > π₯π₯ 2 β 9
(π₯π₯ + 1)2 > (π₯π₯ + 2)2
2
3
2
οΏ½π₯π₯ + 5π₯π₯ β 6 < 0
2π₯π₯ + 3 > π₯π₯ + 2
β1 < π₯π₯ < 1
2
οΏ½π₯π₯ β 7π₯π₯ + 12 β₯ 0
π₯π₯ β 2 β€ 8
π₯π₯ β€ 3 β¨ 4 β€ π₯π₯ β€ 10
2
οΏ½ π₯π₯ + 5π₯π₯ β 6 < 0
2π₯π₯ β 5 > π₯π₯ + 20
β6 < π₯π₯ < 1
π₯π₯ + 50 > 10π₯π₯
οΏ½(π₯π₯ β 3)2 + 3π₯π₯ 2 β 4 < (2π₯π₯ β 1)2
(π₯π₯ + 3)2 > π₯π₯ 2 β 7π₯π₯ + 9
2 < π₯π₯ <
2
οΏ½ π₯π₯2 β π₯π₯ β 6 β€ 0
π₯π₯ + 3π₯π₯ β 4 < 0
β2 β€ π₯π₯ < 1
2
οΏ½ π₯π₯ 2β 9π₯π₯ > 0
5π₯π₯ β 7π₯π₯ + 1 > 0
π₯π₯ < 0 β¨ π₯π₯ > 9
50
9
1 di 5
Algebra
12
13
14
15
16
17
18
19
20
21
v 3.0
Sistemi di disequazioni di secondo grado
2π₯π₯ + 1 2 β π₯π₯
β
>1
3
οΏ½ 25
π₯π₯ β 6π₯π₯ + 7 < 0
π₯π₯ 2 β 8π₯π₯ + 15 > 0
2 < π₯π₯ < 3
π₯π₯ + 2 π₯π₯ π₯π₯ β 4
+ <
β§
3
2
βͺ 4
2π₯π₯ β 3
5π₯π₯ β 2
+1>
β¨
2
βͺ 3
β© π₯π₯ 2 β 2π₯π₯ β 3 > 0
βπ₯π₯ β ππ
1
1 π₯π₯ 1
π₯π₯ οΏ½π₯π₯ β οΏ½ < π₯π₯ 2 β
β +
οΏ½
4
36 3 12
3π₯π₯ + 2 > 4π₯π₯(π₯π₯ β 1)
1
2
β < π₯π₯ <
4
3
β
3(4π₯π₯ + 1)(4π₯π₯ β 1) > 6 β π₯π₯ 2
οΏ½
3(π₯π₯ 2 β 2) < 43
7
< π₯π₯ < β
β3
3
7
< π₯π₯ <
7
β3
π₯π₯ > 2
6(π₯π₯
β 1) β 1 > π₯π₯(π₯π₯ β 2)
οΏ½
π₯π₯(π₯π₯ β 2) β€ 4(π₯π₯ β 1) β 5
3
β¨
7
π₯π₯ = 3
π₯π₯ + 3 > 0
οΏ½ 4π₯π₯ 2 β π₯π₯ + 1 > 0
π₯π₯ 2 + π₯π₯ β 2 β₯ 0
β3 < π₯π₯ β€ β2 β¨
π₯π₯ β₯ 1
π₯π₯ 2 + 3π₯π₯ + 2 > 0
οΏ½4(π₯π₯ + 1) > 1 β π₯π₯ 2
π₯π₯ 2 + π₯π₯ + 1 < 0
ππππππππππππππππππππππ
2π₯π₯(π₯π₯ + 5) > 3(π₯π₯ + 1)2
οΏ½π₯π₯ 2 + 4π₯π₯ + 3 > 3(π₯π₯ β 1)2
π₯π₯ 2 β 16 < (2π₯π₯ β 7)2
1 < π₯π₯ < 3
(π₯π₯ β 1)2 < (2π₯π₯ + 1)(π₯π₯ + 1)
2
οΏ½ 12π₯π₯ + π₯π₯ β 1 > 0
π₯π₯ (π₯π₯ + 2)(2π₯π₯ β 3)
π₯π₯ 2 + 6π₯π₯ < 6 + +
8
4
2π₯π₯ 2 > 3(9 β π₯π₯)
π₯π₯ β 5
64
οΏ½ π₯π₯
< 5π₯π₯ +
5
5
(π₯π₯ + 4)(2π₯π₯ + 5) > 0
β12 < π₯π₯ < β5 β¨
1
3
< π₯π₯ <
4
4
1 < π₯π₯ < 32
2 di 5
Sistemi di disequazioni di secondo grado
Algebra
22
23
24
25
26
27
28
29
30
31
v 3.0
2
οΏ½π₯π₯ 2 β 5π₯π₯ + 6 > 0
π₯π₯ β 16 < 0
β4 < π₯π₯ < 2 β¨
3 < π₯π₯ < 4
2
οΏ½3π₯π₯2 β 5π₯π₯ β 2 > 0
π₯π₯ β 4π₯π₯ + 3 < 0
2 < π₯π₯ < 3
οΏ½
7π₯π₯(π₯π₯ + 2) β 2 > π₯π₯ + 4(5π₯π₯ 2 β 3π₯π₯) + 5(5π₯π₯ β 3)
2(π₯π₯ + 6) + π₯π₯ 2 β€ 2π₯π₯(2π₯π₯ + 1)
β§
βͺ
(3π₯π₯ β 5)2 < 12π₯π₯ β 5
1 2
(2π₯π₯ + 1)(2π₯π₯ β 3) β 4π₯π₯ + 6 > οΏ½π₯π₯ + οΏ½
2
β¨
2
βͺ2π₯π₯ β π₯π₯ β 7 > 4π₯π₯ β 1
4
2
2(5π₯π₯ 2 β 9) < 6π₯π₯ 2 + 63
π₯π₯
οΏ½
3π₯π₯ β 2 β€ 5 β
2
2(π₯π₯ β 2)
π₯π₯ β 1
β₯ π₯π₯ β 1 +
3
2
2
1
1
β¨
(π₯π₯
β© 3 οΏ½π₯π₯ + 3οΏ½ > οΏ½π₯π₯ β 3οΏ½ β 3)
βπ₯π₯ β ππ
9 + β3
< π₯π₯ < 3
6
9
β < π₯π₯ β€ 2
2
4 + β19
β¨
3
β19 β 4
< π₯π₯ β€ 17
3
β§2π₯π₯ β
π₯π₯ < β
7 3
β (4π₯π₯ β 1) β₯ (3π₯π₯ β 1)2
4
2
οΏ½
π₯π₯
2
11
π₯π₯
2π₯π₯ 2 β > π₯π₯ 2 β οΏ½π₯π₯ β οΏ½ β
2
5
10
10
βπ₯π₯ β ππ
1
3
> π₯π₯ + (π₯π₯ β 5)
οΏ½
2
2
π₯π₯(π₯π₯ + 8) β 27 β€ 3(π₯π₯ β 1)
3π₯π₯ β
β8 β€ π₯π₯ β€ 3
5
π₯π₯
π₯π₯(π₯π₯ β 2) + π₯π₯ > 6(π₯π₯ β 1) β
2
2
οΏ½
(π₯π₯ + 1)2 π₯π₯ 2 β 1
3
2π₯π₯ 2 β 11
2
+
β 3π₯π₯ β€ (π₯π₯ + 1) β
3
2
2
3
π₯π₯
π₯π₯
(π₯π₯ + 1) β π₯π₯ β > 2 β π₯π₯ 2 + 2(π₯π₯ + 1)
οΏ½2
2
π₯π₯(π₯π₯ β 5 + 2π₯π₯ β 10) < 0
β1 β€ π₯π₯ < 2 β¨ π₯π₯ > 3
3 + β33
< π₯π₯ < 5
3
3 di 5
Algebra
32
33
34
35
36
37
38
39
40
41
42
v 3.0
οΏ½
Sistemi di disequazioni di secondo grado
(3π₯π₯ β 5)(2π₯π₯ β 5) > (π₯π₯ + 3)(π₯π₯ β 1)
4(π₯π₯ 2 β 1) < 4π₯π₯ β 1
1
1
1
2 οΏ½π₯π₯ β οΏ½ π₯π₯ + 2π₯π₯ β > 4 οΏ½π₯π₯ β οΏ½
οΏ½
2
3
3
(π₯π₯ β 1)2 + 1 < 3(1 β π₯π₯)
β1 β β5
1
< π₯π₯ <
2
2
π₯π₯
(π₯π₯ + 1) β 3π₯π₯ + 5 > 2
οΏ½2
π₯π₯ 2 + 3π₯π₯ β 4 > 0
π₯π₯ < β4 β¨
1 < π₯π₯ < 2 β¨
π₯π₯ > 3
1
3
1
π₯π₯
οΏ½π₯π₯
+
οΏ½
β
3π₯π₯
β
1
<
β
π₯π₯
β
οΏ½
2
2
4
2
2π₯π₯ β 3π₯π₯ + 4 > 0
1
3
β < π₯π₯ <
2
2
1
1
1
2 οΏ½π₯π₯ β οΏ½ π₯π₯ + 2π₯π₯ β > 4 οΏ½π₯π₯ β οΏ½
οΏ½
2
3
3
(π₯π₯ β 1)2 + 1 < 3(1 β π₯π₯)
β1 β β5
1
< π₯π₯ <
2
2
π₯π₯
(π₯π₯ + 1) β 3π₯π₯ + 5 > 2
οΏ½2
π₯π₯ 2 + 3π₯π₯ β 4 > 0
π₯π₯ < β4 β¨
1 < π₯π₯ < 2 β¨ π₯π₯ > 3
1
3
1
π₯π₯
οΏ½π₯π₯
+
οΏ½
β
3π₯π₯
β
1
<
β
π₯π₯
β
οΏ½
2
2
4
2
2π₯π₯ β 3π₯π₯ + 4 > 0
1
3
β < π₯π₯ <
2
2
5
2
(3π₯π₯ + 1)2 β€ οΏ½π₯π₯ β οΏ½ + 1 + π₯π₯
3
3
οΏ½
2 4
(3π₯π₯ β 2)π₯π₯ + π₯π₯ β < β 2π₯π₯
3 3
ππππππππππππππππππππππ
1 2 (π₯π₯ β 3)2
3 β 10π₯π₯
β§οΏ½π₯π₯ β οΏ½ +
β 33 >
2
4
4
1
1
β¨
β©π₯π₯ οΏ½π₯π₯ β 2οΏ½ < 2
π₯π₯ 2 1 β 6π₯π₯ 2 4 β π₯π₯ 2
β§ β
>
2
12
3
2π₯π₯ + 1
β¨π₯π₯(π₯π₯ + 4)
β
1
<
π₯π₯
β
9
3
(π₯π₯ 2 β 1) 2
π₯π₯ β 5
β (π₯π₯ + 1) >
2
3
6
οΏ½
π₯π₯ + 1 2π₯π₯ β 3
+
β€ π₯π₯ 2 β 1
2
4
1
7
β < π₯π₯ <
2
5
ππππππππππππππππππππππ
β3 < π₯π₯ < β
β17
β¨
4
β17
< π₯π₯ < 2
4
π₯π₯ β€ β
1
β¨ π₯π₯ > 2
2
4 di 5
Sistemi di disequazioni di secondo grado
Algebra
43
44
45
46
47
48
49
50
v 3.0
3π₯π₯ 2 β 2π₯π₯ + 7 < 0
1
7
οΏ½
2π₯π₯ οΏ½2π₯π₯ β οΏ½ > π₯π₯ + 5
3
4
ππππππππππππππππππππππ
π₯π₯ 2 π₯π₯ + 1
+
> β2
2
5
2
β¨π₯π₯ β 2 π₯π₯ β 1
β
<3
2
β§
βπ₯π₯ β β
2
οΏ½ π₯π₯ β 5π₯π₯ < 0
π₯π₯ β 2 > 0
2 < π₯π₯ < 5
π₯π₯ 2 + 2π₯π₯ β 3 > 0
19 7
οΏ½π₯π₯ +
β₯
2
2
2
π₯π₯ + π₯π₯ β 12 β₯ 0
6 < π₯π₯ < β4 β¨ π₯π₯ > 3
π₯π₯ + 3 2π₯π₯ + 9
>
6
οΏ½ 2
2(π₯π₯ + 2) β 4 < 3(π₯π₯ + 2) β 7
2π₯π₯ + 3(π₯π₯ + 2) < 16
1 < π₯π₯ < 2
5
π₯π₯
< π₯π₯(π₯π₯ + 1) +
2
2
οΏ½
2 β π₯π₯ 2 β 4π₯π₯ π₯π₯ + 5 (2π₯π₯ β 3)(π₯π₯ β 1)
<
β
5
2
10
β1 < π₯π₯ < 3
οΏ½
ππππππππππππππππππππππ
(π₯π₯ + 1)2 β
3π₯π₯ 2 β 8π₯π₯ + 5 >
π₯π₯ 2π₯π₯ β 1
+
>3
2
3
(5π₯π₯ β 8)2 β (4π₯π₯ β 7)2
3
3 2 9
β§ οΏ½π₯π₯ + οΏ½ β₯
βͺ
2
4
7 3
β¨π₯π₯ + <
4 4
βͺ
β©(π₯π₯ + 5)2 = π₯π₯ + 5
π₯π₯ = β5; π₯π₯ = β4
5 di 5
```
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