REN LUYEN TlT DUY SANG TAO CHO HOC SINH THONG QUA VIEC KHAITHAC CAC BAI TOAN O ThS NGUYEN VU THANH" Trong dqy hqc d phd riidng ndi ehung vd dqy hqc todn ndl riing, vl|c bdi dudng, rin luv|n, phdl Hlln[.]
REN LUYEN TlT DUY SANG TAO CHO HOC SINH THONG QUA VIEC KHAITHAC CAC BAI TOAN O ThS NGUYEN VU THANH" rong dqy hqc d phdriidngndi ehung vd dqy Cdch (phuong phdp veeto): D BDT ois|o|.|6|, suy hqc sinh (HS) Id rdt cdn riilll Theo ede nhd ldm ll hqc, eon ngudi ehl tu duv Keh eye dung trudc Ai.2 mdt khd khdn vl ni/3-jS2 Ddu bdng xdyrakhi vd chf TDST eho cdc em: x-2 Bdi kidn xudt phdl (BTXP) Cddl 7: Xll hdm sd y - J7^+S^ vdt B7XP: ChOng minh rdng, vdi mqi xslu] riii Jx^+.^^S2 (1) ãHudng )(ô> dyng dllu kl|ncd nghllm cOa D l chOng minh bdt ddngriiiie(BDT) (1), GV mdl phuang Hinh (PT) bdc hai): Gqi T Id Idp gid ed rill hudng dfin HS gidi bdng nhllu cdch khde y,£T^y,=4ir-i+^li^ nhou: Cdch (si> dyng phip blln ddl hA3ng HIeOahdmsdyvd duong): (i)»V(jt-ix3-j)si«(:.-2)'iO (ludn dOng) PT y,.4ii^*-l3^ cd nghllm i [ y ] Ddu bdng xdy vd ehl x - Cddl (phuong phdp ddnh gid): Dac6: A' 2*2^t-(x-2)' s* =»,(S2 **|>.'-2.2V(»-lX3-x) ^|i'-4»*3*ioi-2)'-» Ddu bdng xdy vd chi x - Cdch {dp dyng BDT Cd Si): • Hudng I: Ta T ed: V ( » - I ) i s ^ ; V O ^ ^ S Iqi Iheo vl vdi vl'; jddedng Hudng 2: ^'•2+2;(»-lX3-j)S2+(:t-l)+(3-i).4=>y(£2 Ddu bdng xdy vd ehl x - Cddl 4: Ap dyng BOT Bunhloodpxkl: Ddu bdng xdy vd chl x - - Hudng (sd dyng dilu ki|n ed nghi|m ciio h| PT ddl xOng): Ta Hm yj d l PT y, = V ; r ^ + ^ cd nghllm Ddl u = 4x^'i -Ji-x, vdi iiaO,vso, (ll + v=v [•'*'>'>, ta duqc h| FT j ' + , J ° Vv.io '-2)- HI PT * M i l TIPT aq«l nil Ctal - M Tih Guv Tjp Chi BIto dye s6 291 on i I / M M I cd nghllm khdng dm vd chi PT Khal Hide BTXP TO BTXP, llnh hoqt chuyin hudng tu duy, ndng •f'-J'.'f•^J(.^'^-2) = 0ed hoi nghllm khdng dm eao ddn mOe dd khd khdn, to cd Hilriiuduqc ede bdi todn sou: Dllu ndy hrong duong vdi: Bdt lodn I: Tim gid Hj km nhd't, nhd nhdt eOo li = yl-2iy',-2)iO blluriirie A.J^t,in "f o^., Trong ede cdch gidi cOo BTXP, ki dd Km duqe y;-2i0 tdp gid tr| eOa hdm sd y.JT^+^IT^ Id - Hudng {su dyng ddrii|hdm sd): Thye hl|n r.[,fi;2] ninmin ^ = ^2 v d m a x A - Idp ludn nhu hudng ta Km y,dl h| sou ed nghlfkn Bd/todn 2: Xdc d|nh m dl PT VJTf+TJT; , „ [K + V = ^ , cd nghllm bdng phuong phdp dS rii| {hinh 2): \l'*"'" Bdi lodn 3: Gidl vd bl|n ludn PT: H| PT ed nghllm khodng cdch dfO;d;Kr tdm O dio dudng Hdn (d PT u= + v= - din dudng riidng A: u -f V = y„ Hida mai:CIHsd(0,A) sOA > / * - l + -y3-jc-ff( Sdltodn4: Xdc djnh gid H| nhd nhdt cOa m d l bd't PT V r n ' + , ^ S m ihda mdn vdi VIE[1;3] Bdi lodn 5: - Hudng I: Xdc d|nh m dl bdt PT •Jx^+S^i:m cd nghllm?; - Hudng 2; Xdc djnh m d l bdt PT J^TA+S^^mriidamdn oisHsVJoVisj'.si vdi V I e (l;3] ?; - Hudng 3: Xdc d|nh m dl bd't PT Hudng 4: Cdch (phuong phdp luqng gide): Tu dilu •Jx^+~l3^im cd nghllm?; kiln i x s =>-Isx • 2s1, d d i x - = eos a; Xdc d|nh m dl bdt PT V x ^ + > / ^ £ m itido aE[0,]i] To cd: mdn vdt Vie[l;3]? A.Jl.m.a+.Jl-ta.a.^itoi—*aa—}~2m(— 7)51 IDd'u Bdf todn d: Gidl PT: Vr:T+Vn=x'-4xt6 bdng xdy vd chl Sdl todn 7: Xdc dinh m d l PT: a X X Cdch 9; Dot ,, - VJ^-I->/3^ • Jir^*j3^+^(x-r)(3-x)=ni ed nghllm? GV ed rill hudng dfin HS gidi bditodn7bdng cdch: Cdch 1: Dilu ki|n cuo bdi todn Id: i€[l;3] "2V«M^ 2^3-1 2V(;[-1X3-I)(VI:-1-I-T/3-I:) / = e» X - Bdng blln riiiln: Ddl i.,im+,l3^ ^(x-W-x) = ~— vdi i€[S;2], suy ro Bdi lodn chuyin song vl|c Hm m d l PT (' + 2»-2 = 2ii) cd nghi|m te[^;21 TO ddy, ngudi hqc di ddng Hm duqc kit qud cOo bdi todn To dd suy ra: y/2^yi2 Cdch 10 (phuong phdp phdn ehung): Gid sd HI:;)e[1:3] tfido mdn: ^Xi,-l+^i-x„>2 To cd: Cdc/.2:Ddtr=,/r^+V3^ TacdhlPT: P.m-S f.i(S'-2) vdli Tap chi Blao dpc s6 pa i • t / M m # Tuy nhlln, vl|c gidl h| d l Hm m phue Iqp hon gidi tdl uu nhdt Thdng quo vl|e h| Hidng hda ede bdi tdp vd xll bdi lodn dudi nhllu gdc df Hong cdch khdc nhau, GV rin luy|n duqe eho HS khd ndng Md rdng ede bdt todn Md ring t d l todn J: Tim gid H| kim nhdt eOo v^n dyng linh hoqt cdc hoqt djng W h)| nhu: phdn Keh, tdng hqp, HOu hrqng hdo, dde bl|l hdmsd y = V « ^ - f V ^ ndo, , chuyin H> ede hoqt ddng H/duy ndv song Cdch / (phuong phdp dqi sd'|: Ddl hoqt dfng h; khde, khdng suy nghT rdp niudn, B = VxM;v = V r ^ , la cd h| PT mdy mdc Tu dd, HS hungriiOhqc Idp, Keh eye Km tdi, khdm phd d l gidl quylt vdn di vd rin luyin duqe TDST Hong hqc Idp Q u-t-v= V li+v = y >Li, vdt li'+v'=2* T i l lltu Iham khdo iy Nguyin B&Kim Phumig phip dyy hoc mAnToAn NXB Dfl hfc suphifm, H 2007 nghllm cOo PT: X yX*^'0 TO ddy, HS Bdi Vin Ngh| Vtn dvng II lu(n vdo thvc Uh d«y hoc mdn Todn d-tmdug phi tliOng NXB i^l Ape 5if di dingrimduqc gid Ht kin nhdl eOa y - X - 2.phdm, H 2009 Cdch 2: To ed / - o X Xll bdng blln SUMMAIiV riilln: In order for students to practise creative thtnUno a • ^ teachers need to help students to Itnow how to systemtzeltwirlmowledge and apply rtfferentskllls In solving math problems They should not be encourogedtoacceptthefamSlarmethodsbuthave to find out new ones, especially towards a problerr) which requires txith multiple and optimized methods, will be able to generate Interests tor students sd ki T - (0; 2] Vdy maxwhich The enthusiasm In leaning and solvlrtgnnathspioblBm will Improve and sustain teachers' and students' 1: Tim gid H| nhd nhdt, creative thinking S * • II ' ; • II - Tdp gid H| eOa hdm y-2khlx-2 Td'ng qudI bdt lodn Idn nhdt cOo hdm sd>.=.^C^+^^^ Hln[l;3) Pbdf tr^Ai bdt lodn I (riieo hudng khdc): Tim (Tlip tbeo trang 31} gid trj nhd nhd't, Idn nhd't cda hdm sd'