GEOmETRIA 77 x 2 + y2 = 4 {y 2x = 2 [(0 ; 2), (5 ; 5)] _8_ _6_ 87 78 x 2 + y2 = 16 {y = 4 [(0 ; 4)] 88 79 x 2 + y2 = 13 {x + y = 5 [(2 ; 3), (3 ; 2)] 89 80 x 2 + y2 = 25 {x + y = 7 [(3 ; 4), (4 ; 3)] 81 x 2 + y2 = 100 {y 2x = 4 14 48 ___ ___ [(6 ; 8), ( 5 ; 5 )] x 2 + y2 = 169 82 {y = 2x + 2 33 56 ___ ___ [(5 ; 12), ( 5 ; 5 )] x 2 + y2 = 16 83 {y = 2x 4 84 2 2 2 2 16 ___ 12 ___ [(0 ; 4), ( 5 ; 5 )] x + y = 16 {x + y + 4 = 0 [(0 ; 4), ( 4 ; 0)] x + y = 34 85 {x y = 2 2 86 2 91 __ { 3x + 2y = 2 3 __ 3 (2 ; 0), 1 ; ___ ( [ 2 )] x y=3 {xy 4 = 0 x y=8 {xy = 15 2x + 3y = 15 {xy = 9 x+y 2=0 {xy = 8 18 ___ 21 ___ [(0 ; 3), (11 ; 11)] [( 1 ; 4), (4 ; 1)] [(5 ; 3), (3 ; 5)] _3_ [( 9 ; 1), (2 ; 6)] [( 2 ; 4), (4 ; 2)] 92 x 2 y2 = 3 {x + y = 3 [(2 ; 1)] 93 x 2 y2 = 5 {x y = 5 [(3 ; 2)] 94 4x 2 y2 4 = 0 {y + 2x = 0 95 3x 2 5y2 = 28 {y = x 10 [( 3 ; 5), (5 ; 3)] x + 4y 4 = 0 __ 90 3x y 3 = 0 {2x2 + y2 9 = 0 y2 x 2 = 39 96 2 14 {y = _3_ x + ___ 3 [ ] [( 6 ; 4), ( 44 ; 34)] 31 ___ 44 ___ [(5 ; 8), ( 5 ; 5 )] Trova algebricamente le soluzioni reali dei seguenti sistemi di secondo grado in due incognite. Qualora occorra, stabilisci le condizioni per riscrivere il sistema in forma intera. 97 98 y+x=1 {xy + 2y = 2 [(0 ; 1), ( 1 ; 2)] y+x=1 {xy 3x = 1 [( 1 ; 2)] _____ 1 1 _____ x+y + x y =2 104 3 4 _____ + _____ = 7 x + y x y [(1 ; 0)] x + 2y = 2 99 [(0 ; 1), (4 ; 1)] {(x + y)(x y) = 2x(x 2) 1 105 x 2 + y2 = 7 + x y {x = 4 y 2x = 1 y 100 {x 2 = 3 x + x y 106 x 2 + y2 4xy = 142 {x y = 4 [ ] 107 (x + y)2 + x + y = 0 {x + y = 0 [indeterminato] 108 3x 2 4xy + 2y = 76 + 3x 2y2 {2x 3y + 3 = 0 4x 2 + 4y2 = 17x y 101 {x + y = 10 17xy x 2 + y2 = ____ 102 4 {x + y = 15 103 492 _1_ _1_ = _1_ y x 6 {x y = 1 [( 1 ; 3), (1 ; 1)] [(2 ; 8), (8 ; 2)] [(3 ; 12), (12 ; 3)] [(3 ; 2), ( 2 ; 3)] _1_ _1_ _9_ + = 2 109 x y x y = 0,¯ 3 [(3 ; 1), (1 ; 3)] 72 ___ 37 ___ [(9 ; 7), ( 11 ; 11)] _1_ _2_ _2_ _1_ [(9 ; 9), (3 ; 3)]