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(6)(7,42)1.a2+b2=1,b2+c2=2,c2+a2=2.ab+bc+ca().(A)3-12(B)-3+12(C)-3-12(D)3+122.20.:5,0,-2.,.().(A)(B)2(C)4(D)3.ABC,ADBC,MNABAC,MDN=90.BM2+CN2=DM2+DN2,,AD2AB2+AC2().(A)AD2AB2+AC2(B)AD2AB2+AC2(C)AD2=AB2+AC2(D)AD2AB2+AC24.n,,3,4,7,,3n+1,320.n().(A)125(B)126(C)127(D)1285.1.,ABC1,x1x2x3ABBCCA(,,).().(A)x1x2x3(B)x1x3x2(C)x2x3x1(D)x3x2x116.x1x2x3x4(x1x2,x3x4).a,y1=x2-4x+ax(x1,0)(x2,0),y2=x2+ax-4x(x3,0)(x4,0).ABCD,AB=BC=CD,a().(A)a=-3(B)a0(C)a=0(D)a0(7,28)21.2,ADBC,ABCD180,EAB,FBC,AF1220071DC,AFEDBDGH.BCAD=m(mN).GHD,m.2.1,2,,k2(1),1,,(k-1)2,,k.k.112kk+1k+22k(k-1)k+1(k-1)k+2k23.3,ABCDOr,3()XYZW.SX+SZSY+SW(,SUU).4.,,20.,,.(20)y=x2+2mx-n2.(1)(1,1),m,n+4P,P;(2)mn,,,,:,.(25)4,PPAPB,AB,P4CD,BPAACADEF.:BE=BF.(25)1a1a2an21n.4aiajakamai+am=aj+ak(1ijkmn),(a1,a2,,an)n.(1)n=7?;(2)n=8?.1.B.c=32,a=12,b=12.ab+bc+ca=(a+b+c)2-(a2+b2+c2)2,|a+b+c|.|a+b+c|,a=b=-12,c=32.,ab+bc+ca-3+12.2.D.,2019:(1)171283;(2)53,1361,111;22(3)23,9,,51.3.B.55,BACNDE.ME.BD=DC,ED=DN,BEDCND.,BE=CN.,MDEN,EM=MN.BM2+BE2=BM2+CN2=DM2+DN2=MN2=EM2,BEM,MBE=90.,ABC+ACB=ABC+EBC=90.,BAC=90.,AD2=12BC2=14(AB2+AC2).4.D.(1+3n)5=2+3(n-3)5,,n,3,8,13,18,5,52,55,58,511,.5125,251125,.(52)(55)(58)(577)=532A,,A5.,577=3n+1.n=128.5.C.x1=50+x3-55=x3-5,x1x3.,x1x2,x3x2.6.C.x1x2x3x4,x1x3x2x4,x1x3x4x2,x3x4x1x2,x3x1x4x2,x3x1x2x4.6,36(,,a=-4.,x1=x3,x2=x4,).4,|x2-x1|=|x4-x3|.,16-4a=a2+16.a=0-4().a=0.1.25.6,BKAFEDK,6KEBGEA.GHAG=GHBK=HDBD=FCBC=ADBC=1m.,SABD=1m+1SABCD=180m+1,SAHD=1mSABD=180m(m+1),SGHD=1m+1SAHD=180m(m+1)2.180m(m+1)2,,(m+1)2|180.180=22325,m+1=2,36.,m+1=36.2.12k(k2+1).1:212k12k12k3000kkk(k-1)k(k-1)k(k-1)k,123.,k,S=(1+2++k)+[0+k++(k-1)k]=12k(k+1)+12k2(k-1)=12k(k2+1).3.+2-2.7(a)Z.7AB,7(b)3220071,,SX+SZ,SY+SW(XYZWr2).,SX+SZSY+SW.,AC,.7(c),RtABDBD,ABDOA,,SZ,SX+SZ,12r2+r2.SY+SW,12r2-r2.,SX+SZSY+SW12r2+r212r2-r2=+2-2.4.21.20,x.x=15,621;x=16,562122,12;x=17,45621,2223,13;x=18,3,4,5621,22,2324,14;x=19,2,3,4,5621,22,23,2425,15;x=20,1,2,3,4,5621,22,23,24,2526,16.,21.21.(1)(1,1)m=n22.m-(n+4)=n22-(n+4)=12(n2-2n-8)=12(n-4)(n+2),,P=n22,n-2n4;n+4,-2n4.,n=-2,Pmin=2.(2),A(x1,0)B(x2,0)C(0,-n2).x1x2=-n2,n=0,,x1x2=-n20.,x1x2.|x1x2|=n21,,P0(0,1)|OA||OB|=|OP0||OC|.ABCP0,P0(0,1).88,BCBABD.,ABC=PAC=E.ABCAEB.,BEBC=ABAC,BE=ABBCAC.ABF=PAB=ADB,,ABFADB.,BFBD=ABAD,BF=ABBDAD.,PBCPDB,PCAPAD,,BCBD=PCPB,ACAD=PCPA.PA=PB,,BCBD=ACAD.,BCAC=BDAD.BE=BF.(1)n=7,{1,2,3,5,8,13,21},n=7.(2):81a1a2a821,4aiajakamai+am=aj+ak,aj-ai=am-ak(1ijkm8).,8872=28aj-ai42(1ij8),8121,,1aj-ai20(1ij8),20.,8.(i)8,14,aj-ai=am-ak(1ijkm8)..(ii)8,42,42(aj-ai=am-akaj=akai=am).,(ai,aj,ak),2aj=ai+ak(1ijk8).88(ai1,aj1,ak1),(ai2,aj2,ak2),,(ai8,aj8,ak8),,2ajl=ail+akl(l=1,2,,8).a1a8,6.,82,aj1=aj2.ai1+ak1=2aj1=2aj2=ai2+ak2,,ai1ak1ai2ak2(,).(i)(ii),n=8.(,210008)(7)(7,42)1.a1,a2,,an09,n+1a1a2an222a1a2an.n().(A)15(B)16(C)17(D)182.910,22().().(A)913711(B)916(C)912(D)9143.ABCDE,A=C=90,AB=BC=DE=AE+CD=3.().(A)9(B)1015(C)12(D)13154.x,yy1=2x,y2=x+3,y3=-x+3.y().(A)2(B)3(C)5(D)65.y=ax2+bx+c,,(1,0)(0,2).a().(A)a0(B)a-1(C)-2a0(D)-1a06.GABC,rABC,GBCCAABGDGEGF.s=1GD+1GE+1GF.().(A)s3r(B)s=3r(C)s3r(D)(7,28)1.6n(n+1)(n+2)(n+3)5220071