2005年全国初中数学竞赛四川赛区初赛

2005(7,42)1.ab,,().(A)ab]a2b2(B)ab]a2b2(C)|a|b]a2b2(D)a|b|]a2b22.a+b+c=3,a2+b2+c2=3.a2005+b2005+c2005().(A)0(B)3(C)22005(D)32200513.,,(1).12,().(A)16(B)18(C)20(D)224.RtABC,AB=5,BCACx2-(2m-1)x+4(m-1)=0.m().(A)4(B)-1(C)4-1(D)-4125.2,x=1y=ax2+bx+c.().(A)a+b+c0(B)ba+c(C)c2b(D)abc06.,.k.y=x-3y=kx+k,k().(A)2(B)4(C)6(D)8(7,28)1.x,x12+x-12=a.x2+1x=.2.a,xx2+a2x+a=0.x.3.POAB,PCOC,APCACQ.PQC=.4.n,ab,n=a+b+ab,n.,3=1+1+11,3.,12020,.(20)ABy=2x2+4x-2,AB.AB.3(25)3,ABO,AB=d,AOC,AC=AB,OCOD,BDACE.AE.3220062©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.(25)x=a+b-c,y=a+c-b,z=b+c-a,abc.x2=y,z-y=2,abc.1.D.a=-1,b=-2,(A)(C);a=-1,b=1,(B).2.B.0=3(a2+b2+c2)-(a+b+c)2=(a-b)2+(b-c)2+(c-a)2,a=b=c=1.a2005+b2005+c2005=3.3.C.,33,5,1253=20.4.A.(2m-1)2-24(m-1)=25.m1=4,m2=-1().5.C.a0,-b2a=1,b0;2f(-1)=a-b+c0,f(1)=a+b+c0,c0,(A)(B)(D).cb-a=b+b22b,(C).6.C.y=x-3,y=kx+k,x=k+31-k=-1+41-k.k=-3,-1,0,2,3,5.1.a2-2.x12+x-12=ax+x-1+2=a2.x2+1x=x+x-1=a2-2.2.322.a,a0,aa2x+a+x2=0.,=1-4x30.x322.a=0,x=0.43.45.4,OC.PCOC,OCPC.OA=OC,,OAC=OCA=12POC.APQ=CPQ=12APC,PQC=PAQ+APQ=12(POC+APC)=1290=45.4.12.n+1=a+b+ab+1=(a+1)(b+1),n2211.2214,6,8,9,10,12,14,15,16,18,20,2112,n12:3,5,7,8,9,11,13,14,15,17,19,20.55,A(a,b).AB,AB,B(-a,-b).AB,,b=2a2+4a-2,-b=2a2-4a-2.a=1,b=4a=-1,b=-4.A(1,4)A(-1,-4),B(-1,-4)B(1,4).42©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.=ABDA.AB=AC,AE=CD.1=4,CDADE.CD2=CECA,AE2=CECA.AE=x,CE=d-x.,x2=d(d-x),x2+dx-d2=0.AE=x=5-12d.(a,b,c)=12(x+y),12(x+z),12(y+z).y=x2,,a=12(x+x2),b=12(x+z),c=12(x2+z).x=-11+8a2.x,1+8a=T2,T.,2a=T-12T+12.a,T+12=a,T-12=2.,T=5,a=3.a=3x=2,x=-3.x=2,y=x2=4,z-2=2,z=16.b=9,c=10,bc,.x=-3,y=9,z-3=2,z=25.b=11,c=17.abc=31117=561.()2005(5,30)1.ABC,a2+b2=6c2,(cotA+cotB)tanC().(A)15(B)25(C)17(D)272.f(x)R0.abRf(ab)=af(b)+bf(a),f(x)().(A)(B)(C)(D)3.(x,y):(1,1),(1,2),(2,1),(1,3),(2,2),(3,1),(1,4),(2,3),(3,2),(4,1),,x+y,x+y,x.(m,n)(mn)().(A)2m+n-1(B)2m+n-2(C)(m+n-1)(m+n)2+m(D)(m+n-2)(m+n-1)2+m14.1,ABCD-A1B1C1D1,EFABAA1.CEB1D1FB1().5220062©1994-2007ChinaAcademicJournalElectronicPublishingHouse.Allrightsreserved.