sujet

(1)

FRQFRXUV JHQHUDO 4<<5

H{huflfh L

Rq glw tx*xqh sduwlh qrq ylgh gx sodq S hvw frqyh{h vl hooh srvvëgh od sursulìwì vxlydqwh = Srxu wrxw frxsoh +P> Q, gh srlqwv gh > oh vhjphqw ^PQ` hvw frqwhqx gdqv

Vrlw xqh sduwlh frqyh{h gx sodq S= Vl D hvw xq srlqw gh S> ã wrxw frxsoh +P> Q, gh srlqwv gh rq dvvrflh oh srlqw p gìql sdu

Dp @ 4₅PQ hw rq qrwh D+, o*hqvhpeoh ghv srlqwv p dlqvl rewhqxv1

41 d , Prqwuhu txh D+, dgphw xq fhqwuh gh v|pìwulh1

e , D txhooh frqglwlrq d0w0rq D+, @ B

f , Vrlhqw E hw F ghx{ srlqwv gx sodq S1 Sdu txhooh wudqvirupdwlrq sdvvh0w0rq gh E+, ã

F+, B

51 Vrlw D xq srlqw gx sodq S= Gìwhuplqhu hw uhsuìvhqwhu D+, oruvtxh =

d , hvw xqh edqgh gx sodq S gìolplwìh sdu ghx{ gurlwhv sdudooëohv1 e , hvw gìolplwìh sdu xq wuldqjoh1

f , hvw xq ghpl0glvtxh1

61 Prqwuhu txh gdqv ohv ghx{ fdv 51e, hw 51f,/ ohv frqwrxuv gh hw D+, rqw od píph orqjxhxu1

H{huflfh LL Vrlw +F, xq fhufoh gx sodq gh ud|rq 4=

41 Gìwhuplqhu ohv wuldqjohv DEF lqvfulwv gdqv oh fhufoh +F, srxu ohvtxhov od vrpph DE5_{. EF}5_{. FD}5

hvw pd{lpdoh1

51 Gìwhuplqhu ohv txdgulodwëuhv DEFG lqvfulwv gdqv oh fhufoh +F, srxu ohvtxhov od vrpph DE5_{. DF}5_{. DG}5_{. EF}5_{. EG}5_{. FG}5

hvw pd{lpdoh1 Uhsuìvhqwhu xq who txdgulodwëuh1 H{huflfh LLL

Vrlw DEFG xq wìwudëguh lqvfulw gdqv xqh vskëuh gh fhqwuh R= Rq qrwh J o*lvredu|fhqwuh ghv txdwuh vrpphwv gx wìwudëguh hw L oh fhqwuh gh od vskëuh lqvfulwh gdqv oh wìwudëguh1 Prqwuhu txh ohv wurlv sursulìwìv vxlydqwhv vrqw ìtxlydohqwhv =

41 Ohv ghx{ srlqwv R hw J vrqw frqirqgxv1

51 Ohv txdwuh idfhv gx wìwudëguh vrqw lvrpìwultxhv1 61 Ohv ghx{ srlqwv R hw L vrqw frqirqgxv1

H{huflfh LY

Vrlw +xq, od vxlwh qxpìultxh gìqlh sdu od grqqìh gh vhv ghx{ suhplhuv whuphv x3 hw x4> 3 ? x3 ? 4

hw 3 ? x4? 4> hw od uhodwlrq gh uìfxuuhqfh =

xq.5@ 4₅sxq.4.sxq

41 Prqwuhu txh od vxlwh +xq, hvw frqyhujhqwh hw gìwhuplqhu vd olplwh1

51 Prqwuhu tx*ã sduwlu g*xq fhuwdlq udqj q3> od vxlwh +xq, hvw prqrwrqh + rq qh ghpdqgh sdv gh

gìwhuplqhu q3 txl gìshqg ghv ydohxuv lqlwldohv x3 hw x4= ,

H{huflfh Y