Centrale Maths 1 MP 2017 — Énoncé 1/4
kyRd@yj@jy R9,kR,Rk S;2 Rf9
kyRd
Ji?ûKiB[m2b R
JS
9 ?2m`2b *H+mHi`B+2b miQ`Bbû2b
am` H T`iB2 bvKûi`B[m2 /ǶmM2 Ki`B+2
LQiiBQMb
aBԝ2iԟbQMi /2b 2MiB2`b Mim`2Hb MQM MmHb- QM MQi2෧։Ӵ නHǶ2bT+2 p2+iQ`B2H /2b Ki`B+2b `û2HH2b ¨ԝHB;M2b 2i ԟ+QHQMM2b 2i෧։ නHǶ2bT+2 p2+iQ`B2H /2b Ki`B+2b +``û2b෧։Ӵ։ නX PM /û}MBi /2 7ÏQM MHQ;m2෧։Ӵ ජ2i ෧։ ජX
G i`MbTQbû2 /ǶmM2 Ki`B+2Ӷ/2෧։Ӵ න2bi MQiû2ӶળX PM `TT2HH2 [mǶmM2 Ki`B+2Ӷ/2෧։ න2bi /Bi2 bvKûi`B[m2bBӶળ Ӷ2i [mǶ2HH2 2bi /Bi2MiBbvKûi`B[m2bBӶળ ਲӶX
G2 bQmb@2bT+2 p2+iQ`B2H /2෧։ න+QMbiBimû /2b Ki`B+2b bvKûi`B[m2b 2bi MQiû෭։ නX G2 bQmb@2bT+2 p2+iQ`B2H /2෧։ න+QMbiBimû /2b Ki`B+2b MiBbvKûi`B[m2b 2bi MQiûෛ։ නX
G2 ;`QmT2 /2b Ki`B+2b Q`i?Q;QMH2b ¨ԝHB;M2b 2iԝ+QHQMM2b 2bi MQiû0։ නX PM MQi2Ӿ։H Ki`B+2 B/2MiBiû /Mb෧։ නX
SQm` iQmi2 Ki`B+2 +``û2Ӷ ୩ ෧։ න- QM MQi2Ӷ֎φϵ Ӷ Ӷળ2iӶռφϵ Ӷ ਲ ӶળX BMbB-Ӷ֎2bi mM2 Ki`B+2 bvKûi`B[m2-Ӷռ2bi mM2 Ki`B+2 MiBbvKûi`B[m2 2iӶ Ӷ֎ ӶռX PM /Bi [m2Ӷ֎2bi HT`iB2 bvKûi`B[m2/2Ӷ2i [m2Ӷռ2bi bT`iB2 MiBbvKûi`B[m2X
SQm`Ӷ ୩ ෧։ න- QM MQi2TQන ӶH2 bT2+i`2 `û2H /2Ӷ- +Ƕ2bi@¨@/B`2 HǶ2Mb2K#H2 /2b pH2m`b T`QT`2b `û2HH2b /2ӶX lM2 Ki`B+2 bvKûi`B[m2 `û2HH2 2bi /Bi2TQbBiBp2bB b2b pH2m`b T`QT`2b bQMi TQbBiBp2b 2i 2HH2 2bi /Bi2/û}MB2 TQbBiBp2 bB b2b pH2m`b T`QT`2b bQMi bi`B+i2K2Mi TQbBiBp2bX
PM MQi2෭։ නHǶ2Mb2K#H2 /2b Ki`B+2b bvKûi`B[m2b TQbBiBp2b /2෧։ න2i෭։ නHǶ2Mb2K#H2 /2b Ki`B+2b bvKûi`B[m2b /û}MB2b TQbBiBp2b /2෧։ නX
P#D2+iB7
GǶQ#D2+iB7 /m T`Q#HĕK2 2bi /Ƕûim/B2` +2`iBM2b T`QT`Bûiûb /2b Ki`B+2b `û2HH2b +``û2b /QMi H T`iB2 bvKûi`B[m2 2bi /û}MB2 TQbBiBp2X
G T`2KBĕ`2 T`iB2 TTQ`i2 [m2H[m2b `ûbmHiib T`ûHBKBMB`2bX
G /2mtBĕK2 T`iB2- Qɍ QM ûim/B2 H2b Ki`B+2b ӻ@bBM;mHBĕ`2b- 2i H i`QBbBĕK2 T`iB2- [mB i`Bi2 /2b Ki`B+2b TQbBiBp2K2Mi bi#H2b- bQMi H`;2K2Mi BM/ûT2M/Mi2bX
A _ûbmHiib T`ûHBKBMB`2b
AX Ĝ .BbiM+2 /2٘¨٘۰
PM KmMBi෧։ න/m T`Q/mBi b+HB`2 +MQMB[m2 /QMMû T` Ԃ ԃ ޓ US Ԃળԃ QɍUS/ûbB;M2 H i`+2X PM MQi2 ઢ਼ઢϵH MQ`K2 2m+HB/B2MM2 bbQ+Bû2X
AXXRV JQMi`2` [m2෭։ න2i ෛ։ න bQMi /2mt bQmb@2bT+2b p2+iQ`B2Hb bmTTHûK2MiB`2b Q`i?Q;QMmt /Mb ෧։ න2i T`û+Bb2` H2m`b /BK2MbBQMbX
AXXkV aQBiӶ ୩ ෧։ නX JQMi`2` [m2 TQm` iQmi2 Ki`B+2Ԉ ୩ ෭։ න-ઢӶ ਲ Ӷ֎ઢϵହ ઢӶ ਲ ԈઢϵX S`û+Bb2` ¨ [m2HH2 +QM/BiBQM bm`Ԉ ୩ ෭։ න- +2ii2 BMû;HBiû 2bi mM2 û;HBiûX
AX" Ĝ oH2m`b T`QT`2b /2٘۰ PM +QMbB/ĕ`2Ӷ ୩ ෧։ නX
AX"XRV aBԂ ୩ ෧։ න2iԍ Ԏ ୩ ෧։Ӵφ න- H Ki`B+2ԍળԂ ԎTT`iB2Mi ¨෧φ න2i QM +QMpB2Mi /2 HǶB/2MiB}2`
m MQK#`2 `û2H û;H ¨ bQM mMB[m2 +Q2{+B2MiX
p2+ +2ii2 +QMp2MiBQM- KQMi`2` [m2 Ӷ֎ ୩ ෭։ න bB 2i b2mH2K2Mi bB ԍ ୩ ෧։Ӵφ න- ԍળӶ֎ԍ 2i [m2 Ӷ֎୩ ෭։ නbB 2i b2mH2K2Mi bBԍ ୩ ෧։Ӵφ න ੨ \^-ԍળӶ֎ԍ X
AX"XkV SQm` iQmi2 pH2m` T`QT`2 `û2HH2ᅱ/2Ӷ- KQMi`2` [m2NJO TQන Ӷ֎ ହ ᅱ ହ NBY TQන Ӷ֎X 1M /û/mB`2 [m2 bBӶ֎୩ ෭։ නHQ`bӶ2bi BMp2`bB#H2X
AX"XjV PM bmTTQb2 [m2Ӷ֎୩ ෭։ නX
V JQMi`2` [mǶBH 2tBbi2 mM2 mMB[m2 Ki`B+2ӷ/2෭։ නi2HH2 [m2ӷϵ Ӷ֎X
#V JQMi`2` [mǶBH 2tBbi2 mM2 Ki`B+2Ԇ/2ෛ։ නi2HH2 [m2EFU Ӷ EFU Ӷ֎ EFU Ӿ։ ԆX +V 1M /û/mB`2 [m2EFU Ӷ EFU Ӷ֎X
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Centrale Maths 1 MP 2017 — Énoncé 2/4
kyRd@yj@jy R9,kR,Rk S;2 kf9
AX"X9V PM bmTTQb2ӶBMp2`bB#H2 2i- +QM7Q`KûK2Mi mt MQiiBQMb /m T`Q#HĕK2- Ӷਲφ֎/ûbB;M2 H T`iB2 bvKû@
i`B[m2 /2 HǶBMp2`b2 /2ӶX JQMi`2` [m2ऺEFU ӶऻϵEFUऺ Ӷਲφ֎ऻ EFU Ӷ֎X PM TQm`` +QMbB/û`2`Ӷ Ӷਲφ֎ӶળX
AX* Ĝ S`iB2 bvKûi`B[m2 /2b Ki`B+2b Q`i?Q;QMH2b
AX*XRV aQBiӶ ୩ 0։ නX JQMi`2` [m2 H2b pH2m`b T`QT`2b /2Ӷ֎bQMi /Mb<ਲ >X
AX*XkV .QMM2` mM 2t2KTH2 /2 Ki`B+2 bvKûi`B[m2Ԉ/Mb෭ϵ නi2HH2 [m2TQන Ԉ ଢ଼ <ਲ >2i TQm` H[m2HH2 BH MǶ2tBbi2 Tb /2 Ki`B+2Ӷ ୩ 0ϵ නpû`B}MiӶ֎ ԈX
AX*XjV aQBiԈ ୩ ෭։ නX
V PM bmTTQb2 [m2TQන Ԉ ଢ଼ <ਲ >2i [m2 TQm` iQmi2 pH2m` T`QT`2ᅱ/2Ԉ/Mb>ਲ <- HǶ2bT+2 T`QT`2 /2Ԉ bbQ+Bû ¨ᅱ2bi /2 /BK2MbBQM TB`2X JQMi`2` [mǶBH 2tBbi2Ӷ ୩ 0։ නi2HH2 [m2Ӷ֎ ԈX
#V _û+BT`Q[m2K2Mi- KQMi`2` [m2 bǶBH 2tBbi2Ӷ ୩ 0։ නi2HH2 [m2Ӷ֎ Ԉ- HQ`bTQන Ԉ ଢ଼ <ਲ >2i TQm` iQmi2 pH2m` T`QT`2ᅱ/2Ԉ/Mb>ਲ <- HǶ2bT+2 T`QT`2 /2ԈbbQ+Bû ¨ᅱ2bi /2 /BK2MbBQM TB`2X
AA Ji`B+2b ٝ@bBM;mHBĕ`2b
.Mb H bmBi2 /2 +2ii2 T`iB2- QM MQi2Ӻ։ ෧։Ӵφ න[mǶQM KmMBi /m T`Q/mBi b+HB`2 ਼ ] ਼/û}MB T`
ԍ Ԏ ୩ Ӻ։ ԍ ] Ԏ ԍળԎ Qɍ- +QKK2 m AX"XR- QM B/2MiB}2 H Ki`B+2ԍળԎ¨ bQM mMB[m2 +Q2{+B2MiX
aB ହ ԟ ହ ԝ- QM MQi2։Ӵ නHǶ2Mb2K#H2 /2b Ki`B+2b /2෧։Ӵ න/2 `M; û;H ¨ԟX lM2 Ki`B+2 /2෧։ න2bi /Bi2bBM;mHBĕ`2bB 2HH2 MǶ2bi Tb BMp2`bB#H2X
aBӻ2bi mM bQmb@2bT+2 p2+iQ`B2H MQM `û/mBi ¨\^/2Ӻ։2i bBԀ ୩ ෧։ න- QM /Bi [m2Ԁ2biӻ@bBM;mHBĕ`2bǶBH 2tBbi2ԍ ୩ ӻMQM MmH i2H [m2ԏ ୩ ӻ-ԏળԀԍ X .Mb H2 +b +QMi`B`2- QM /Bi [m2Ԁ2biӻ@`û;mHBĕ`2X
AAX Ĝ *b Qɍٝ2bi mM ?vT2`THM
AAXXRV JQMi`2` [mǶmM2 Ki`B+2 /2෧։ න2bi bBM;mHBĕ`2 bB 2i b2mH2K2Mi bB 2HH2 2biӺ։@bBM;mHBĕ`2X
.Mb +2ii2 bQmb@T`iB2 AAX- QM bmTTQb2 /ûbQ`KBbԝ X aQBiӻ ӽmM ?vT2`THM /2Ӻ։2i bQBiԃ ୩ Ӻ։mM p2+i2m` mMBiB`2 MQ`KH ¨ӽX
AAXXkV JQMi`2` [m2Ӷ2biӽ@bBM;mHBĕ`2 bB 2i b2mH2K2Mi bǶBH 2tBbi2 mM p2+i2m` MQM MmHԍ/2ӽ2i mM `û2Hᅱi2Hb [m2Ӷԍ ᅱԃX
AAXXjV 1M /û/mB`2 [m2Ӷ2biӽ@bBM;mHBĕ`2 bB 2i b2mH2K2Mi bB H Ki`B+2Ӷկ ন Ӷ ԃԃળ ୩ ෧։φ න2bi bBM;mHBĕ`2X
.Mb H2b [m2biBQMb bmBpMi2b-Ӷ2bi mM2 Ki`B+2 BMp2`bB#H2 /2෧։ නX AAXX9V JQMi`2` [mǶBH 2tBbi2 mM2 Ki`B+2ӷ ন ӷφ ӷϵ
ӷϯ ӷΚp2+ӷφ୩ ෧։ න-ӷϵ୩ ෧։Ӵφ න-ӷϯ୩ ෧φӴ։ න- ӷΚ୩ ෧φ නi2HH2 [m2 ,Ӷկӷ ন Ӿ։
ԃળӶਲφ ਲԃળӶਲφԃ X AAXX8V 1M /û/mB`2 [m2EFU Ӷկ ਲԃળӶਲφԃ EFU ӶX
AAXXeV JQMi`2` [m2 bBEFUऺ Ӷਲφ֎ऻ - HQ`b BH 2tBbi2 mM ?vT2`THMӽ/2Ӻ։i2H [m2Ӷ2biӽ@bBM;mHBĕ`2X AAXXdV 1M /û/mB`2 [m2 bBEFU Ӷ֎ - HQ`b BH 2tBbi2 mM ?vT2`THMӽ/2Ӻ։i2H [m2Ӷ2biӽ@bBM;mHBĕ`2X AAXX3V PM bmTTQb2 [m2Ӷ֎୩ ෭։ නX JQMi`2` [m2Ӷ2biӽ@`û;mHBĕ`2 TQm` iQmi ?vT2`THMӽ/2Ӻ։X
AAX" Ĝ 1t2KTH2 PM i`Bi2` HǶ2t2KTH2
Ӷ Ӷ ᅲ ৄৃ
ূ
ਲ ᅲ ਲ ᅲ ਲ ਲ ᅲ ᅲ ਲ
ਲ
ে
AAX"XRV JQMi`2` [m2Ӷ ᅲ2bi BMp2`bB#H2 TQm` iQmi `û2HᅲX
AAX"XkV *H+mH2`Ӷ ᅲ֎2i KQMi`2` [m2Ӷ ᅲ֎2bi bBM;mHBĕ`2 TQm`ᅲ - ਲఀ - ఀ
X AAX"XjV .ûi2`KBM2` mM ?vT2`THMӽi2H [m2Ӷ bQBiӽ@bBM;mHBĕ`2X
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Centrale Maths 1 MP 2017 — Énoncé 3/4
kyRd@yj@jy R9,kR,Rk S;2 jf9
AAX* Ĝ *b Qɍٝ2bi /2 /BK2MbBQMٿ ਲ
PM bmTTQb2 B+Bԝ X aQBiӻmM bQmb@2bT+2 p2+iQ`B2H /2Ӻ։/2 /BK2MbBQMԝ ਲ X PM +QMbB/ĕ`2 ԃφ ԃϵmM2
#b2 /2ӻર2i QM TQb2
ԃ ऺ ԃφ ԃϵऻ ୩ ෧։Ӵϵ න
AAX*XRV JQMi`2` [m2Ӷ2biӻ@bBM;mHBĕ`2 bB 2i b2mH2K2Mi bǶBH 2tBbi2 mM ûHûK2Mi MQM MmHԍ/2ӻ2i /2mt `û2Hbᅱφ- ᅱϵi2Hb [m2Ӷԍ ᅱφԃφ ᅱϵԃϵX
AAX*XkV 1M /û/mB`2 [m2Ӷ2biӻ@bBM;mHBĕ`2 bB 2i b2mH2K2Mi bB H Ki`B+2
Ӷկ ৄৃৃ
ূ
Ӷ ԃφ ԃϵ
ԃφળ ԃϵળ
ে
ন Ӷ ԃ
ԃળ ϵ ୩ ෧։ϵ න
2bi bBM;mHBĕ`2X
.Mb H2b [m2biBQMb bmBpMi2b-Ӷ2bi mM2 Ki`B+2 BMp2`bB#H2 /2෧։ නX AAX*XjV JQMi`2` [mǶBH 2tBbi2 mM2 Ki`B+2ӷ ন ӷφ ӷϵ
ӷϯ ӷΚp2+ӷφ୩ ෧։ න-ӷϵ୩ ෧։Ӵϵ න-ӷϯ୩ ෧ϵӴ։ න 2iӷΚ୩ ෧ϵ නi2HH2 [m2
Ӷկӷ ন Ӿ։ ԃળӶਲφ ਲԃળӶਲφԃ AAX*X9V 1M /û/mB`2 [m2EFU Ӷկ EFU ԃળӶਲφԃ EFU ӶX
AAX*X8V JQMi`2` [mǶBH 2tBbi2ԅ ୩ ։Ӵϵ නi2HH2 [m2EFU ԅળӶਲφԅ bB 2i b2mH2K2Mi bǶBH 2tBbi2ԅ୩ ։Ӵϵ න i2HH2 [m2EFU ԅળӶԅங X
AAX*XeV JQMi`2` [m2 bBԃ ० ԃφ ԃϵ१HQ`b
EFU ԃળӶԃங ԃφળӶ֎ԃφ ԃϵળӶ֎ԃϵ ਲ ԃφળӶ֎ԃϵϵ ԃφળӶռԃϵϵ AAX*XdV 1M /û/mB`2 [m2 bBӶ֎୩ ෭։ න- HQ`bEFU ԃળӶਲφԃ X
AAX*X3V 1M +QM+Hm`2 [m2 bBӶ֎୩ ෭։ න- HQ`bӶ2biӻ@`û;mHBĕ`2 TQm` iQmi bQmb@2bT+2 p2+iQ`B2Hӻ/2 /BK2MbBQM ԝ ਲ /2Ӻ։X
AAX. Ĝ 1t2KTH2
PM `2T`2M/ HǶ2t2KTH2 /2 H bQmb@T`iB2 AAX" p2+ᅲ X
AAX.XRV *QKK2Mi +?QBbB`ԃ ० ԃφ ԃϵ१/2 7ÏQM [m2EFU ԃળӶԃங \
AAX.XkV .ûi2`KBM2` mM bQmb@2bT+2 p2+iQ`B2Hӻ/2Ӻϯi2H [m2EJN ӻ 2i i2H [m2Ӷ bQBiӻ@bBM;mHBĕ`2X
AAX1 Ĝ *b ;ûMû`H
aQBiӻmM bQmb@2bT+2 p2+iQ`B2H /2Ӻ։/2 /BK2MbBQMԝ ਲ ԟ- Qɍ ହ ԟ ହ ԝ ਲ X
AAX1XRV JQMi`2` [m2Ӷ2biӻ@bBM;mHBĕ`2 bBEFU ԃળӶԃங TQm` mM2 Ki`B+2ԃ୩ ։Ӵ න[m2 HǶQM /û}MB`X PM bmTTQb2 /ûbQ`KBb [m2Ӷ֎୩ ෭։ නX
AAX1XkV JQMi`2` [m2 bBԍ ୩ ෧Ӵφ න2bi MQM MmH HQ`bԍળԃળӶԃԍ X
AAX1XjV 1M /û/mB`2 [m2 H2b pH2m`b T`QT`2b `û2HH2b /2ԃળӶԃbQMi bi`B+i2K2Mi TQbBiBp2bX AAX1X9V 1M /û/mB`2 [m2EFU ԃળӶԃங X
AAX1X8V 1M /û/mB`2 [m2Ӷ2biӻ@`û;mHBĕ`2 TQm` iQmi bQmb@2bT+2 p2+iQ`B2Hӻ ଃ \^/2Ӻ։X
AAA Ji`B+2b TQbBiBp2K2Mi bi#H2b
PM /Bi [mǶmM2 Ki`B+2Ӷ/2෧։ න2biTQbBiBp2K2Mi bi#H2bB iQmi2b b2b pH2m`b T`QT`2b +QKTH2t2b QMi mM2 T`iB2
`û2HH2 bi`B+i2K2Mi TQbBiBp2X AAAX Ĝ 1t2KTH2b
AAAXXRVaQBiӶ ୩ ෧ϵ නX JQMi`2` [m2Ӷ2bi TQbBiBp2K2Mi bi#H2 bB 2i b2mH2K2Mi bBUS Ӷ 2iEFU Ӷ X AAAXXkV
V G bQKK2 /2 /2mt Ki`B+2b TQbBiBp2K2Mi bi#H2b /2෧ϵ න2bi@2HH2 Mû+2bbB`2K2Mi TQbBiBp2K2Mi bi#H2 \
#V aQBiӶ-ӷ/Mb෧։ න/2mt Ki`B+2b TQbBiBp2K2Mi bi#H2b [mB +QKKmi2MiX JQMi`2` [m2Ӷӷ2bi TQbBiBp2K2Mi bi#H2X
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Centrale Maths 1 MP 2017 — Énoncé 4/4
kyRd@yj@jy R9,kR,Rk S;2 9f9
AAAXXjVaQBiӶ ୩ ෧։ නi2HH2 [m2Ӷ֎bQBi /û}MB2 TQbBiBp2X
V aQBiԍ Ԏ JԏmM2 Ki`B+2 +QHQMM2 /2෧։Ӵφ ජ- QɍԎ2iԏTT`iB2MM2Mi ¨෧։Ӵφ නX PM TQb2ԍ Ԏ ਲ Jԏ 2i QM B/2MiB}2 H Ki`B+2ԍળӶԍ ୩ ෧φ ජm MQK#`2 +QKTH2t2 û;H ¨ bQM mMB[m2 +Q2{+B2MiX
JQMi`2` [m2- bBԍ ଃ - HQ`b3F ԍળӶԍ - Qɍ3F ԩ/ûbB;M2 H T`iB2 `û2HH2 /2ԩ ୩ ජX
#V JQMi`2` [m2Ӷ2bi TQbBiBp2K2Mi bi#H2X
AAAXX9V.QMM2` mM 2t2KTH2 /2 Ki`B+2ӶTQbBiBp2K2Mi bi#H2 i2HH2 [m2Ӷ֎MǶ2bi Tb /û}MB2 TQbBiBp2X AAAX" Ĝ .Mb +2ii2 bQmb@T`iB2 AAAX"- QM ûi#HBi mM `ûbmHii bm` HǶ2tTQM2MiB2HH2 /2 Ki`B+2 [mB b2` miBH2 T` H bmBi2X
PM `TT2HH2 [m2- TQm` iQmi2 Ki`B+2Ԃ ୩ ෧։ ජ- HǶ2tTQM2MiB2HH2 /2Ԃ2bi /û}MB2 T`
FYQ Ԃ
ֆЈ
Ԃֆ Ԛ
G 7QM+iBQMԣ ޓ FYQ ԣԂ2bi /û}MB2 2i /2 +Hbb2ෝbm`න2i b 7QM+iBQM /û`Bpû2 2bi /QMMû2 T`
ԣ ޓ Ԃ FYQ ԣԂ FYQ ԣԂԂ /2 THmb-FYQ ਲԣԂ FYQ ԣԂ Ӿ։TQm` iQmi `û2HԣX
AAAX"XRVaQBiᅱ ୩ ජi2H [m23F ᅱ X aQBiԤmM2 7QM+iBQM ¨ pH2m`b +QKTH2t2b /2 +Hbb2ෝφbm`නX PM bmTTQb2 [m2 H 7QM+iBQMԥ Ԥ ᅱԤ2bi #Q`Mû2 bm`නX JQMi`2` [m2Ԥ2bi #Q`Mû2 bm`නX
PM TQm`` +QMbB/û`2` HǶû[miBQM /Bzû`2MiB2HH2Ԩ ᅱԨ ԥX
AAAX"XkVaQBiԉ ୩ ෧։ ජ mM2 Ki`B+2 i`BM;mHB`2 bmTû`B2m`2 ¨ +Q2{+B2Mib +QKTH2t2bX PM bmTTQb2 [m2 H2b +Q2{+B2Mib /B;QMmt /2ԉbQMi /2b MQK#`2b +QKTH2t2b /2 T`iB2 `û2HH2 bi`B+i2K2Mi TQbBiBp2X aQBiԤφ w Ԥ։/2b 7QM+iBQMb ¨ pH2m`b +QKTH2t2b- /û}MB2b 2i /2 +Hbb2ෝφbm`න2i bQBi- TQm` iQmiԣ ୩ න-
Ԋ ԣ ৄৃ
ূ Ԥφ ԣ Ԥ։ੂ ԣ
ে
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AAAX"XjVaQBiӶ ୩ ෧։ නmM2 Ki`B+2 TQbBiBp2K2Mi bi#H2 /2 pH2m`b T`QT`2b +QKTH2t2bᅱφ w ᅱ։2i bQBiᅦmM
`û2H i2H [m2 ᅦ NJOφହօହ։3F ᅱօX
JQMi`2` [m2 H 7QM+iBQMԣ ޓ Fᆺ֏FYQ ਲԣӶ2bi #Q`Mû2 bm`නX
PM TQm`` TTHB[m2` H [m2biBQM AAAX"Xk ¨ mM2 Ki`B+2 i`BM;mHB`2ԉb2K#H#H2 ¨Ӷ ਲ ᅦӾ։X
AAAX* Ĝ lM2 +`+iû`BbiBQM /2b Ki`B+2b TQbBiBp2K2Mi bi#H2b
aQBiӶ ୩ ෧։ නmM2 Ki`B+2 TQbBiBp2K2Mi bi#H2X PM +QMbB/ĕ`2 HǶ2M/QKQ`T?BbK2ဃ/2෧։ නi2H [m2
Ԃ ୩ ෧։ න ဃ Ԃ ӶળԂ ԂӶ
AAAX*XRVJQMi`2` [m2ဃ2bi TQbBiBp2K2Mi bi#H2- +Ƕ2bi@¨@/B`2 [m2 b Ki`B+2 /Mb mM2 #b2 [m2H+QM[m2 /2෧։ න 2bi TQbBiBp2K2Mi bi#H2X
AAAX*XkV
V JQMi`2` [mǶBH 2tBbi2 mM2 mMB[m2 Ki`B+2ӷ ୩ ෧։ නi2HH2 [m2Ӷળӷ ӷӶ Ӿ։X
#V JQMi`2` [m2ӷ2bi bvKûi`B[m2 2i [m2EFU ӷ X
AAAX*XjVSQm` iQmi `û2Hԣ- QM TQb2ԋ ԣ FYQ ਲԣӶળ FYQ ਲԣӶ2iԌ ԣ
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ԋ Ԣ EԢX
V JQMi`2` [m2- TQm` iQmi `û2Hԣ-ԋ ԣ ୩ ෭։ න2i [m2- bBԣ -Ԍ ԣ ୩ ෭։ නX
#V JQMi`2` [m2- TQm` iQmi `û2Hԣ-ӶળԌ ԣ Ԍ ԣӶ Ӿ։ਲ ԋ ԣX
+V ZmǶQ#iB2Mi@QM 2M 7BbMi i2M/`2ԣp2`b/Mb HǶû;HBiû T`û+û/2Mi2 \ 1M /û/mB`2 [m2 H Ki`B+2ӷ/2 H [m2biBQM AAAX*Xk 2bi /û}MB2 TQbBiBp2X
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