Esercizi sui sistemi di secondo grado
Francesco Daddi - 3 settembre 2010
1)
x 2 Ÿ2 y2 3 xŸ y2 sol x1 y1 ; x5 3 y1 3 2) 3 x 2 4 y2 x0 x2 y1 sol x1 y1 ; x1 2 y1 4 3) 4 x 2 Ÿ2 y2 60 x y sol x1 y1 ; x1 y1 4) 2 x 2 6 x yx 3 xŸ5 y2 sol x0 y2 5 ; x1 4 y1 4 5) 5 x 2 y2 Ÿ4 y2 xŸ20 x y1 sol x3 2 y5 2 ; x1 2 y1 2 6) x yx 2 Ÿ2 y2 y2 x xŸ y0 sol x0 y0 7) 3 x y2 x2Ÿ2 x yŸ y20 sol x1 2 y1 2 8) x2 y1 x2Ÿ y22 x1 sol ; x1Ÿ2Ɓ
10 5 yƁ
10 5 x12Ɓ
10 5 yƁ
10 5 9) xŸ y0 x2Ÿ y2x100 sol x2 y2 ; x5 2 y5 2 10) x 2 Ÿ y2 1Francesco Daddi - 3 settembre 2010
Esercizi sui sistemi simmetrici fondamentali
1)
xŸ y4 xy3 sol x3 y1 ; x1 y3 2) xŸ y1 xy7 sol impossibile 3) xŸ y5 xy6 sol x3 y2 ; x2 y3 4) xŸ y5 xy6 sol x1 y6 ; x6 y1 5) xŸ y3 xy4 sol x4 y1 ; x1 y4 6) xŸ y3 xy2 sol x2 y1 ; x1 y2 7) xŸ y4 xy4 sol x2 y2 8) xŸ y6 xy9 sol x3 y3 9) xŸ y2 xy10 sol x1ŸƁ
11 y1Ɓ
11 ; x1Ɓ
11 y1ŸƁ
11 10) xŸ y2 xy10 sol impossibile 11) xŸ y7 xy12 sol x4 y3 ; x3 y4 12) xŸ y5 2 xy7 2 sol x 7 2 y1 ; x1 y7 2 13) xŸ y2 xy1 3 sol x1Ÿ2Ɓ
3 3 y12Ɓ
3 3 ; x12Ɓ
3 3 y1Ÿ2Ɓ
3 3 14) xŸ y4 xy50 sol x2Ÿ3Ɓ
6 y23Ɓ
6 ; x23Ɓ
6 y2Ÿ3Ɓ
6Esercizi sui sistemi simmetrici con grado superiore a 2
Francesco Daddi - 3 settembre 2010
www.webalice.it/francesco.daddi
1) x 3 Ÿ y3 9 xŸ y3 sol x2 y1 ; x1 y2 2) x 3 Ÿ y3 342 xŸ y6 sol x1 y7 ; x7 y1 3) x 3 Ÿ y3 35 xŸ y5 sol x3 y2 ; x2 y3 4) x 4 Ÿ y4 2 xŸ y0 sol x1 y1 ; x1 y1 5) x 4 Ÿ y4 17 xŸ y3 sol x1 y2 ; x2 y1 6) x 5 Ÿ y5 2xŸ y0 sol impossibile
7)
x 3 Ÿ y3 35 x y6 sol x2 y3 ; x3 y2 8) x 3 Ÿ y3 511 8 x y2 sol x4 y1 2 ; x 1 2 y4 9) x 4 Ÿ y4 17 x y2 sol x1 y2 ; x1 y2 ; x2 y1 ; x2 y1 10) x 5 Ÿ y5 64 xŸ y4 sol x2 y2 11) x 4 Ÿ y4 337 x y12 sol x3 y4 ; x4 y3 ; x3 y4 ; x4 y3Francesco Daddi - 4 settembre 2010
Esercizi sui sistemi simmetrici
www.webalice.it/francesco.daddi
1) x 2 Ÿ y2 5 x y2 sol x2 y1 ; x1 y2 ; x2 y1 ; x1 y2 2) xŸ y1 x2Ÿ y21 sol x1 y0 ; x0 y1 3) xŸ y2 x2Ÿ y22 sol x1 y1 4) xŸ y2x2Ÿ y2ŸxŸ y1 sol impossibile
5)
xŸ y3 x2Ÿ y24 x4 y5 sol x4 y1 ; x1 y4 6) x y1 x2Ÿ y2Ÿ3 x y5 sol x1 y1 ; x1 y1 7) x y12 x2Ÿ y225 sol x3 y4 ; x4 y3 ; x3 y4 ; x4 y3 8) 2 xŸ2 y2 4 x2Ÿ4 y252 sol x2 y3 ; x3 y2 9) xŸ y 2 3 4 3 x2Ÿ3 y215 4 sol x1 y1 2 ; x 1 2 y110)
xŸ y2 x2Ÿ y23 x y4 sol x0 y2 ; x2 y0 11) xŸ y7x2Ÿ y26 x y3 x3 y44 sol
x1 2 y13 2 ;
x13 2 y1 2 12) x 2 Ÿ y2 1xŸ y6 sol impossibile
13)
x 2 Ÿ y2 5 x y3 sol impossibile 14) x 2 Ÿ y2 18 xŸ y6 sol x3 y3 15) x 2 Ÿ y2 8 xŸ y3 sol x3Ÿ