Osnovy teorii Galua.

146

746 IV~~~. lpuiwro e-iuq meopuu raAya

JIA R MToO yaBBHeHHq 4)YHKL1Hq1 Z' CBsI3aHa CO CTapofl 4lyH]KLuert Z T~ai:.
Z'=-(4x + 1)(4x, + 1) +(4x + 1)(4x, + 1)=-16 (XlX2+x~x4) +4 (x1~+x. +
+ x3-1-x.) +2 =16z - 2
a n1OTOMY
(1 6z1 - 2)z1+ (I16z - 2)Z2 +(16z13 - 2I)za 16~ 4,
ii = 1z )z1 + (16z, - 2)2Z2 + (16z3 - 2)2z, = 256u - 6~4 C + 8,
a'=(16z - 2)z12 +(16z, — 2)z-22 +(16z, ~2 Z3 2= 16u -24.
HpHHHma~au BO0 BHHmaHme, trro u,i = 16, u =8, nonyqllrm:
=44, Ur 3912, a' 104.
nlOACTaBJ1.qS B (21),roaytinm cJaeapyoluee ypaB~eHn~e Avim 1:
(2.27) 14 -6412 + 641 =0,
Hmeioiuee eAtHHCTBeHHbIPI pa~tHOHaJIbHbIJ AKopeHb I = 0. IlOJLCTaBJIqqu n (2.18) 31aqeHHH1 T ia I, iuonyiymn:
(2.28) Z = 0.
H-OACTaB~JISqf B CHiCTemy (2.16) 3Ha4eHH51 T = - 3, 0 -4, Z =0, nojiytrn4:
-4a, 3a3= 0, 3a2-4a%3-, 3a,,i4, 4, 3(7,0+4a +3 3a0
PeLUHM 9TY CHCTemy:
(2.29) 0ao =0, a, = a0, l, a. =0,
T. e. ypaBeHerne (2.19) nepexOaHT B (2.20) upH nlomoufl czieayuouero npeo6pa3oBaHHRf:
(2.30) X =X2.
~ 3. nOCpoeCHHH flPH UOMOILH IUHPKyJHI H AHHeflKH
1. JRaHO a~nre6pa14iecKoe ypaB~eHnue
(3.1) fW -0
IK094)4IHLieHTbl KOTOpMr H3BeCTHMl (wuin tIHCJneHHOI Him~~ reomeTpHtlecKH,
T. e. 3 aaai-bl, KaK AJIJ1Hbl OTpeP3KOB). Tpe6yeTCui y3HaTb6, MOMM(O Al1i HaR1TH
KOPHH 3Toro ypaBHelHHR, fl01b3ylCb IIOCTpOeHHIIMI I1pH noOMOIH LUMPKYJ5 H
AHHeA~KH4.
H4TO6bI OTBeTHTb, Ha1 STOT BOnipoc, npealBaplTeolb~o JtoKa)Kem
T e o p e M y 74. KaHKaoe ruoc~poeHn~e tU4pKyJ1eM 14 1114efiiol mo)KeT
6wm~ HPHBeaeCH0 K pewieHHIO KBaJIp3THb1X ypaBHeI-HM. O6paTlio, KOPHH
KBaalpaTHoro ypaBeHeHHu Bcerjia MoryT 6b1Tb, Haflteiibi nTOCTpoeBHliM
Hocpe21CTBOM [IJ4PKYA11 H J1HHefimKH
12Ao K a 3a T e lbC TB0. 1 0. Kauviaoe noCTpoeHne uJ1pKyJ1eM 11 JHHeA1KoR
mo)KeT 6blTb pa36HTo Ha a11emeHTapHbie nOCfpoeu-114$1, 143 KOTO~b1X Rawa1Loe
COCTOJIT B Haxo)K.LeHMM1 TO'IKH nepece'ierni JaByx KpyrOB (eCui CIIHTw3T
ripgmyto 4LCTHbIM B14.IOM K~pyra), ieLCHTp H paaH4YC KO6TOpbIX H3BeCTHbl. AHaJIHTH4qecKH aLeJIo 11pBOJLHTCH K HaxO)1{AeHfi4O pewneHHR1 CHACTem ypaBemi~fl
(3.2) ~ ~ f(x -a)2-+- (y -b)2- r2 = O,
(3.2) 1~~~( (- al)2 +C(y-b,)2- r 12 = 0)