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₯ − 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 © 2016 - www.matematika.it 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 − 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 © 2016 - www.matematika.it 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 − 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 32 33 34 35 36 37 38 39 40 41 42 v 3.0 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 4 di 5 Sistemi di disequazioni di secondo grado Algebra 43 44 45 46 47 48 49 50 v 3.0 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 © 2016 - www.matematika.it 5 di 5
