S& GL&O DVC VA DAO TqO KY THI HQC SlNH GTOT THANH PH~ - LOP 9 HA NO1 NAM HQC 2012 - 2013 "* 4N- 1 DC CH~NH THOC 1 Man: Toan NgAy thi: 05/4/2013 Thlri gian Iirm bai: 150 phiit (~e' thi g&n OI trang) a) Tim cic s8 thuc a, b sao cho da thuc 4x4 - 1 Ix3 - 2ax2 + 5bn - 6 chia hit cho triciia P v6i a=4+& vB b=4-&. Bai 2 (5 diem). ~6~~-~' ry+5~+5y 6=0 a) Giai h$ phumg trinh: 120~' -y2 -28~+9=0. b) Tim clc s6 nguygn x, y th6a m2n: lL3 Bli 3 (2 dikm). Cho ba s8 thqc a.6,~ dumg thda m5n - + - + - = 3. Chhg minh: abc Bhi 4 (7 diin). Cho tam gihc AAC co ba g6c nhgn, noi tiip dubng trbn (0) va AB < AC. Cac duhg cao AD, BE, CF clia tarn giac ABC gap nhau tai H. Gpi I la giao diem hai dubng thing EF vB CB. Duhg thbg AI tit (0) tai M (M khhc A). a) Chhg minh n5m diem A, M, F, H, E cung nim trh rn+t duhg tron. b) Goi N Il trung didm cua BC. Chirmg,minh ba di&m M,H,N thkg Mng. c) Chhg minh BM.AC + AM.BC = AB.MC. Bhi 5 (1 dikm). Cho 2013 diem 4,4, ,A,, v8 duhg trbn (0;l) tcy 9 chg nkn trong mat phhg. Chirng minh tren duimg trbn (0; 1) do, ta lu6n c6 the tim duuc mat diim M sao cho MX, + MA, + . + hQ,,, 2 20 13. * f&~ - - - - - - - - - . DVC VA DAO TqO KY THI HQC SlNH GTOT THANH PH~ - LOP 9 HA NO1 NAM HQC 2012 - 2013 "* 4N- 1 DC CH~NH THOC 1 Man: Toan NgAy thi: 05/4 /2013 Thlri gian Iirm. duuc mat diim M sao cho MX, + MA, + . + hQ,,, 2 20 13. * f&~ - - - - - - - - - . (~e' thi g&n OI trang) a) Tim cic s8 thuc a, b sao cho da thuc 4x4 - 1 Ix3 - 2ax2 + 5bn - 6 chia hit cho triciia P v6i a=4+& vB b= 4-& amp;. Bai