Sistemi di disequazioni di secondo grado
Algebra
1
2
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v 3.0
1
(π₯π₯ − 2) + 2π₯π₯
4π₯π₯
−
1
>
οΏ½
3
π₯π₯ 2 − 3π₯π₯ + 2 > 0
1
< π₯π₯ < 1 ∨ π₯π₯ > 2
5
3π₯π₯ 2 ≤ 4π₯π₯ + 7
οΏ½2π₯π₯ − 3 π₯π₯ π₯π₯ − 5
+ <
+3
5
2
2
−1 ≤ π₯π₯ ≤
−π₯π₯(π₯π₯ + 2) > −2
5 − π₯π₯ 5
οΏ½π₯π₯
≤ π₯π₯ −
+
4
2
2
9
4
0 ≤ π₯π₯ < −1 + √3
3π₯π₯ + 1 3
3
(1 + π₯π₯) −
π₯π₯(π₯π₯
−
4)
+
≥
οΏ½
4
4
4
2
3π₯π₯ + 7π₯π₯ + 2 > 0
π₯π₯ < −2 ∨
1
4 − √15
− < π₯π₯ ≤
3
2
4 + √15
∨ π₯π₯ ≥
2
οΏ½
3 < π₯π₯ < −
(π₯π₯ + 3)2 > π₯π₯ 2 − 9
(π₯π₯ + 1)2 > (π₯π₯ + 2)2
2
3
2
οΏ½π₯π₯ + 5π₯π₯ − 6 < 0
2π₯π₯ + 3 > π₯π₯ + 2
−1 < π₯π₯ < 1
2
οΏ½π₯π₯ − 7π₯π₯ + 12 ≥ 0
π₯π₯ − 2 ≤ 8
π₯π₯ ≤ 3 ∨ 4 ≤ π₯π₯ ≤ 10
2
οΏ½ π₯π₯ + 5π₯π₯ − 6 < 0
2π₯π₯ − 5 > π₯π₯ + 20
−6 < π₯π₯ < 1
π₯π₯ + 50 > 10π₯π₯
οΏ½(π₯π₯ − 3)2 + 3π₯π₯ 2 − 4 < (2π₯π₯ − 1)2
(π₯π₯ + 3)2 > π₯π₯ 2 − 7π₯π₯ + 9
2 < π₯π₯ <
2
οΏ½ π₯π₯2 − π₯π₯ − 6 ≤ 0
π₯π₯ + 3π₯π₯ − 4 < 0
−2 ≤ π₯π₯ < 1
2
οΏ½ π₯π₯ 2− 9π₯π₯ > 0
5π₯π₯ − 7π₯π₯ + 1 > 0
π₯π₯ < 0 ∨ π₯π₯ > 9
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Algebra
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v 3.0
Sistemi di disequazioni di secondo grado
2π₯π₯ + 1 2 − π₯π₯
−
>1
3
οΏ½ 25
π₯π₯ − 6π₯π₯ + 7 < 0
π₯π₯ 2 − 8π₯π₯ + 15 > 0
2 < π₯π₯ < 3
π₯π₯ + 2 π₯π₯ π₯π₯ − 4
+ <
β§
3
2
βͺ 4
2π₯π₯ − 3
5π₯π₯ − 2
+1>
β¨
2
βͺ 3
β© π₯π₯ 2 − 2π₯π₯ − 3 > 0
βπ₯π₯ ∈ π
π
1
1 π₯π₯ 1
π₯π₯ οΏ½π₯π₯ − οΏ½ < π₯π₯ 2 −
− +
οΏ½
4
36 3 12
3π₯π₯ + 2 > 4π₯π₯(π₯π₯ − 1)
1
2
− < π₯π₯ <
4
3
−
3(4π₯π₯ + 1)(4π₯π₯ − 1) > 6 − π₯π₯ 2
οΏ½
3(π₯π₯ 2 − 2) < 43
7
< π₯π₯ < −
√3
3
7
< π₯π₯ <
7
√3
π₯π₯ > 2
6(π₯π₯
− 1) − 1 > π₯π₯(π₯π₯ − 2)
οΏ½
π₯π₯(π₯π₯ − 2) ≤ 4(π₯π₯ − 1) − 5
3
∨
7
π₯π₯ = 3
π₯π₯ + 3 > 0
οΏ½ 4π₯π₯ 2 − π₯π₯ + 1 > 0
π₯π₯ 2 + π₯π₯ − 2 ≥ 0
−3 < π₯π₯ ≤ −2 ∨
π₯π₯ ≥ 1
π₯π₯ 2 + 3π₯π₯ + 2 > 0
οΏ½4(π₯π₯ + 1) > 1 − π₯π₯ 2
π₯π₯ 2 + π₯π₯ + 1 < 0
ππππππππππππππππππππππ
2π₯π₯(π₯π₯ + 5) > 3(π₯π₯ + 1)2
οΏ½π₯π₯ 2 + 4π₯π₯ + 3 > 3(π₯π₯ − 1)2
π₯π₯ 2 − 16 < (2π₯π₯ − 7)2
1 < π₯π₯ < 3
(π₯π₯ − 1)2 < (2π₯π₯ + 1)(π₯π₯ + 1)
2
οΏ½ 12π₯π₯ + π₯π₯ − 1 > 0
π₯π₯ (π₯π₯ + 2)(2π₯π₯ − 3)
π₯π₯ 2 + 6π₯π₯ < 6 + +
8
4
2π₯π₯ 2 > 3(9 − π₯π₯)
π₯π₯ − 5
64
οΏ½ π₯π₯
< 5π₯π₯ +
5
5
(π₯π₯ + 4)(2π₯π₯ + 5) > 0
−12 < π₯π₯ < −5 ∨
1
3
< π₯π₯ <
4
4
1 < π₯π₯ < 32
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Sistemi di disequazioni di secondo grado
Algebra
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2
οΏ½π₯π₯ 2 − 5π₯π₯ + 6 > 0
π₯π₯ − 16 < 0
−4 < π₯π₯ < 2 ∨
3 < π₯π₯ < 4
2
οΏ½3π₯π₯2 − 5π₯π₯ − 2 > 0
π₯π₯ − 4π₯π₯ + 3 < 0
2 < π₯π₯ < 3
οΏ½
7π₯π₯(π₯π₯ + 2) − 2 > π₯π₯ + 4(5π₯π₯ 2 − 3π₯π₯) + 5(5π₯π₯ − 3)
2(π₯π₯ + 6) + π₯π₯ 2 ≤ 2π₯π₯(2π₯π₯ + 1)
β§
βͺ
(3π₯π₯ − 5)2 < 12π₯π₯ − 5
1 2
(2π₯π₯ + 1)(2π₯π₯ − 3) − 4π₯π₯ + 6 > οΏ½π₯π₯ + οΏ½
2
β¨
2
βͺ2π₯π₯ − π₯π₯ − 7 > 4π₯π₯ − 1
β©
4
2
2(5π₯π₯ 2 − 9) < 6π₯π₯ 2 + 63
π₯π₯
οΏ½
3π₯π₯ − 2 ≤ 5 −
2
2(π₯π₯ − 2)
π₯π₯ − 1
≥ π₯π₯ − 1 +
3
2
2
1
1
β¨
(π₯π₯
β© 3 οΏ½π₯π₯ + 3οΏ½ > οΏ½π₯π₯ − 3οΏ½ − 3)
βπ₯π₯ ∈ π
π
9 + √3
< π₯π₯ < 3
6
9
− < π₯π₯ ≤ 2
2
4 + √19
∨
3
√19 − 4
< π₯π₯ ≤ 17
3
β§2π₯π₯ −
π₯π₯ < −
7 3
− (4π₯π₯ − 1) ≥ (3π₯π₯ − 1)2
4
2
οΏ½
π₯π₯
2
11
π₯π₯
2π₯π₯ 2 − > π₯π₯ 2 − οΏ½π₯π₯ − οΏ½ −
2
5
10
10
βπ₯π₯ ∈ π
π
1
3
> π₯π₯ + (π₯π₯ − 5)
οΏ½
2
2
π₯π₯(π₯π₯ + 8) − 27 ≤ 3(π₯π₯ − 1)
3π₯π₯ −
−8 ≤ π₯π₯ ≤ 3
5
π₯π₯
π₯π₯(π₯π₯ − 2) + π₯π₯ > 6(π₯π₯ − 1) −
2
2
οΏ½
(π₯π₯ + 1)2 π₯π₯ 2 − 1
3
2π₯π₯ 2 − 11
2
+
− 3π₯π₯ ≤ (π₯π₯ + 1) −
3
2
2
3
π₯π₯
π₯π₯
(π₯π₯ + 1) − π₯π₯ − > 2 − π₯π₯ 2 + 2(π₯π₯ + 1)
οΏ½2
2
π₯π₯(π₯π₯ − 5 + 2π₯π₯ − 10) < 0
© 2016 - www.matematika.it
−1 ≤ π₯π₯ < 2 ∨ π₯π₯ > 3
3 + √33
< π₯π₯ < 5
3
3 di 5
Algebra
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οΏ½
Sistemi di disequazioni di secondo grado
(3π₯π₯ − 5)(2π₯π₯ − 5) > (π₯π₯ + 3)(π₯π₯ − 1)
4(π₯π₯ 2 − 1) < 4π₯π₯ − 1
1
1
1
2 οΏ½π₯π₯ − οΏ½ π₯π₯ + 2π₯π₯ − > 4 οΏ½π₯π₯ − οΏ½
οΏ½
2
3
3
(π₯π₯ − 1)2 + 1 < 3(1 − π₯π₯)
−1 − √5
1
< π₯π₯ <
2
2
π₯π₯
(π₯π₯ + 1) − 3π₯π₯ + 5 > 2
οΏ½2
π₯π₯ 2 + 3π₯π₯ − 4 > 0
π₯π₯ < −4 ∨
1 < π₯π₯ < 2 ∨
π₯π₯ > 3
1
3
1
π₯π₯
οΏ½π₯π₯
+
οΏ½
−
3π₯π₯
−
1
<
−
π₯π₯
−
οΏ½
2
2
4
2
2π₯π₯ − 3π₯π₯ + 4 > 0
1
3
− < π₯π₯ <
2
2
1
1
1
2 οΏ½π₯π₯ − οΏ½ π₯π₯ + 2π₯π₯ − > 4 οΏ½π₯π₯ − οΏ½
οΏ½
2
3
3
(π₯π₯ − 1)2 + 1 < 3(1 − π₯π₯)
−1 − √5
1
< π₯π₯ <
2
2
π₯π₯
(π₯π₯ + 1) − 3π₯π₯ + 5 > 2
οΏ½2
π₯π₯ 2 + 3π₯π₯ − 4 > 0
π₯π₯ < −4 ∨
1 < π₯π₯ < 2 ∨ π₯π₯ > 3
1
3
1
π₯π₯
οΏ½π₯π₯
+
οΏ½
−
3π₯π₯
−
1
<
−
π₯π₯
−
οΏ½
2
2
4
2
2π₯π₯ − 3π₯π₯ + 4 > 0
1
3
− < π₯π₯ <
2
2
5
2
(3π₯π₯ + 1)2 ≤ οΏ½π₯π₯ − οΏ½ + 1 + π₯π₯
3
3
οΏ½
2 4
(3π₯π₯ − 2)π₯π₯ + π₯π₯ − < − 2π₯π₯
3 3
ππππππππππππππππππππππ
1 2 (π₯π₯ − 3)2
3 − 10π₯π₯
β§οΏ½π₯π₯ − οΏ½ +
− 33 >
2
4
4
1
1
β¨
β©π₯π₯ οΏ½π₯π₯ − 2οΏ½ < 2
π₯π₯ 2 1 − 6π₯π₯ 2 4 − π₯π₯ 2
β§ −
>
2
12
3
2π₯π₯ + 1
β¨π₯π₯(π₯π₯ + 4)
−
1
<
π₯π₯
−
β©
9
3
(π₯π₯ 2 − 1) 2
π₯π₯ − 5
− (π₯π₯ + 1) >
2
3
6
οΏ½
π₯π₯ + 1 2π₯π₯ − 3
+
≤ π₯π₯ 2 − 1
2
4
1
7
− < π₯π₯ <
2
5
ππππππππππππππππππππππ
−3 < π₯π₯ < −
√17
∨
4
√17
< π₯π₯ < 2
4
π₯π₯ ≤ −
© 2016 - www.matematika.it
1
∨ π₯π₯ > 2
2
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Sistemi di disequazioni di secondo grado
Algebra
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3π₯π₯ 2 − 2π₯π₯ + 7 < 0
1
7
οΏ½
2π₯π₯ οΏ½2π₯π₯ − οΏ½ > π₯π₯ + 5
3
4
ππππππππππππππππππππππ
π₯π₯ 2 π₯π₯ + 1
+
> −2
2
5
2
β¨π₯π₯ − 2 π₯π₯ − 1
−
<3
β© 7
2
β§
∀π₯π₯ ∈ β
2
οΏ½ π₯π₯ − 5π₯π₯ < 0
π₯π₯ − 2 > 0
2 < π₯π₯ < 5
π₯π₯ 2 + 2π₯π₯ − 3 > 0
19 7
οΏ½π₯π₯ +
≥
2
2
2
π₯π₯ + π₯π₯ − 12 ≥ 0
6 < π₯π₯ < −4 ∨ π₯π₯ > 3
π₯π₯ + 3 2π₯π₯ + 9
>
6
οΏ½ 2
2(π₯π₯ + 2) − 4 < 3(π₯π₯ + 2) − 7
2π₯π₯ + 3(π₯π₯ + 2) < 16
1 < π₯π₯ < 2
5
π₯π₯
< π₯π₯(π₯π₯ + 1) +
2
2
οΏ½
2 − π₯π₯ 2 − 4π₯π₯ π₯π₯ + 5 (2π₯π₯ − 3)(π₯π₯ − 1)
<
−
5
2
10
−1 < π₯π₯ < 3
οΏ½
ππππππππππππππππππππππ
(π₯π₯ + 1)2 −
3π₯π₯ 2 − 8π₯π₯ + 5 >
π₯π₯ 2π₯π₯ − 1
+
>3
2
3
(5π₯π₯ − 8)2 − (4π₯π₯ − 7)2
3
3 2 9
β§ οΏ½π₯π₯ + οΏ½ ≥
βͺ
2
4
7 3
β¨π₯π₯ + <
4 4
βͺ
β©(π₯π₯ + 5)2 = π₯π₯ + 5
π₯π₯ = −5; π₯π₯ = −4
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