PHoNGGrAo DVC vA DAo r4o KY TrrrcHgt\ Hec srNHcrol cAp euAN HONG BANG ZOt: r,{AMHQC ZO1Z DE THI MON: TOAN _ LOP EE CHINH THTTC Thdi gian." I50 philr (kh6rtg ki giao di1 (Ei rhi gim 0t rrang) a - Bii 1:(2.0cli6m) a Chirngminh ,irrg -l - * =1, - + + >24 Vl +V: 45+47 ,19997 +.,19999 b Cho ba s6 a, b, c + th6a mdn: I I I I - ; V ar Vr -a + Vtbr - + { = t [ - ' vt lD ,- , zfva vc J + J i- -_t r chrmg minh ring cdcs6 a, b, c c6 it nh6t mot s6 bing 2l Bii 2: (2.5 cli€m) a Giii phucrngtrinh y3 = 2qf2y -1-1 b chrmg minh khdng t6n tai cFrygiittrf nguyCn(x; y) thoamdn x, - 2y, = 2013 Biri 3: (2.0 cti6m).Cho tri gi6c ABCD o e = 400;D: g00 vir AD : BC Ggi E, F lAn luot lir trung di6m cua AB vd CD Tfnh eFD f Itdi 4: (2.5 eli6m).Tir di€m A nim ngodi duong tron tAm 0, ke hai ti6p tuy6n AB vd AC (B vd c ld titip diem) Ducrngthing qua A cet (o) tqi D vd E (D nim gifra A vd E), k6 day cung EN song songv6i BC, DN cit BC tai I chirng minh rdng BI : cI Bii 5: (1.0 tti6m) cho a,b, c la dg ddi ba canhctram6t tam gi6cthoam6n: C20t3 62013 * ;- a+b-c a-b+c Hdy x5c dinh dang.cfiatam gidc Az0t3 -a+b+c - A2012* 62012 + Qt"' Gidm thi khorcggiai th{chgi th1m PHoNGcrAo uUC,vA DAo rAo oAp Ax va BrEUonim UONroAru- Lope HONG BANG tt+Atu Hec 2orz-2ar3 Bii 1: (2.0eli6m) >24 '19997+ 19999 b Cho ba s6 a, ;e0 thoa mdn - - L - I ^r_ | 1 - va V a V b V c 4li*Vu*i6-Jo* zJi-lze-r24s I _ Chring minh rSng tron g citcs6 a, b, c c6 it nh6tm6t sd bing 27 D6p rln - a)Edt{- 1 -f L +- vl + V3 ,ls + Jt B: .-r Js+Js Jt +Jt Jgggt+ Jgggs 1- l , - j - - ' +Jrooor Jeeee Jz"n -Jz"n Ta c6 - ^ l n + 1+ r / n + n6nA*B: -r Jrooor ViA>Bn6nAt A*B 100-r 99 r2rzo 0,5d 0,5d b) Ta c6 ,^';+ ^r _#b" =i1 c>r(v* * * vu" v;) #.#.# 1 e:(V"u*Vu.*V;)-Vabc=o (1) 0o25aI -"rir(1)vd(z)taco:3(V"b+ Vui * VA)- V"b.+ e($ + Vu fiF 7: o ( $ - r X V o - r x i - ) = o e V a : h o i cV b = 3h o d{c6 = 0,541 YQy itnhAtm6t ba so a, b, c co mQts6 bing27 a Gi6i phuorrgtrinh y3 =2ll2a-y -1 b chrmg minh kh6ng tdn tai cFrygi|tri nguydn(x; y) th6amdn x2 - 2y2= 2013 Daty :?112x= ta c6h6: j[ " ' * l = y- < + {[ * ' * = y '0',25d L y '* : x L t ' y 3= ( y " ) * I:Zy [ x ,+ I : [*' - v ) ( *+' x y +y '* ) -oe ' = , t(" 0,25d ( v ix + x yy+' + = [ * * + J ' !*2, \ 4/ t 0,5d 2b (1.0ili6m) x' =2y' + 2013+ x16,d4tx = 2k+ i;(k e Z)thayvdotac6: 0"25a1 2y' - 4k' + 4k - 2012e y2= 2k2+ 2k-1006 (l)+ y chfin,y = 2t;(t e z) 02sd Thayx;y viro(1) vd bi6nd6i: 2t2:k(k + t) 503 (2) X6t thay vr cria (2) ludn chEn;vp cfia (2) td t6 16vi k(k+t) ch84(Tfch s6 nguydnli6n ti6p).vpy d6u":" crta(2)kh6ngth6xay rac2'lra + caron (:); c2()12 + a20t2 0,25d 6p dr,rngb6t ding thric CoSi cho hai s6 ducrngta c6: a2ot3 I a2or3 + (, - a + b + > r l _ _ ", _ (_u*b+c)aro" -a+b+c ")urr,' v - a + b + c \ = a20t3 _ + c + a t o t t b + a ' o " c > a t o t ,( ) -a+b Tuong tU ta c6: 0,5d ;2013 a-b+c + abr'r,+ br.,rc> 36zotz (5) ^2013 + a c r o '*r a o r>t c o t z ( ) ", a+b-c Tt (1), (2), (3), (4), (5), (6) ta c6 C2013 a+b-c I + b2ot: - 42013 ) u20rz* 62012 + -_: + crorr.p6, rc_':xhy rakhi vd chi a + b + c a-b+c a: b : c tric ld ta c6 tam si6c dAu 0.25d ...PHoNGcrAo uUC,vA DAo rAo oAp Ax va BrEUonim UONroAru- Lope HONG BANG tt+Atu Hec 2orz-2ar3 Bii 1: (2.0eli6m) >24 ' 199 97+ 199 99 b Cho ba s6 a, ;e0 thoa mdn - -... - ' +Jrooor Jeeee Jz"n -Jz"n Ta c6 - ^ l n + 1+ r / n + n6nA*B: -r Jrooor ViA>Bn6nAt A*B 100-r 99 r2rzo 0,5d 0,5d b) Ta c6 ,^';+ ^r _#b" =i1 c>r(v* * * vu" v;) #.#.# 1 e:(V"u*Vu.*V;)-Vabc=o (1)... 6lR =70a 1,0t1 Bii 4: (2.5tti6m).Tt di6mA nim ngodidudngtrdn tAmO, ke hai ti6p tuy6nAB vd AC (B vd c ld ti6p dicm).Dulng thing quaA cat 1o; t4i D vd E (D nim gifraA vd E), ke d6ycungEN songsongv6i