Rèn luyện tư duy sáng tạo cho học sinh thông qua việc khai thác các bài toán

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 hf duy sdng H;io (TDST) cho

hqc sinh (HS) Id rdt cdn riilll. Theo ede nhd ldm ll

hqc, eon ngudi ehl tu duv Keh eye khi dung trudc

mdt khd khdn vl ni<it nhdn riiOc edn phdi khde

phyc, mdt Hnh hudng gql vdn dl. Do dd, gido

vltn (GV) edn tqo ra ede Hnh hudng ed vdn dl

nhdm khol ddy nhOng y h/dng mdl eho HS dl

gidl quylt vdn dl. Mdl Hong nhohg bi|n phdp

hOu hi|u rin luy|n TDST cho HS dd kl: Tip cho

HS gidl <^uy^ vdn di bdng nhiiu phurmg phdp

khdc nhou vd Iva ehqn edeh gidl quyit lot uu

nhdt.

Xudt phdt Ktmdlbditodndongldn dudi ddy,

GV ed rill hudng dfin HS khol riide duqe nhilu

bdi H)dn khde nhou nhdm rin luy|n, phdt Hlln

TDST eho cdc em:

1. Bdi kidn xudt phdl (BTXP)

B7XP: ChOng minh rdng, vdi mqi xslu] riii

Jx^+.^^S2 (1).

Dl chOng minh bdt ddng riiiie (BDT) (1), GV

ed rill hudng dfin HS gidi bdng nhllu cdch khde

nhou: Cdch 1 (si> dyng phip blln ddl hA3ng

duong): (i)»V(jt-ix3-j)si«(:.-2)'iO (ludn dOng).

Ddu bdng xdy ra khi vd ehl khi x - 2.

Cddl 2 (phuong phdp ddnh gid): D<lt A -

,/^tjr^,>ac6: A' .2*2^t-(x-2)' s* =»,(S2.

Ddu bdng xdy ra khi vd chi khi x - 2.

Cdch 3 {dp dyng BDT Cd Si): • Hudng I: Ta

ed: V(»-I)is^; VO^^S - jddedng

Iqi Iheo v l vdi vl'; Hudng 2:

.^'•2+2;(»-lX3-j)S2+(:t-l)+(3-i).4=>y(£2

Ddu bdng xdy ra khi vd ehl khi x - 2.

Cddl 4: Ap dyng BOT Bunhloodpxkl:

Ddu bdng xdy ra khi vd chl khi x - 2.

Cdch 5 (phuong phdp veeto): D<it a = (l;l);

b = y7^:S^y Ti> BDT ois|o|.|6|, suy ra

Ai.2.

Cdch d:Vi dudng Hdn

dudng kfnh AB - 2, tdm O.

Vdi i6(l;3], h-ln AB Idy

dllm H soo eho AH - X -

l,BH-3-x(fen/i/|.

TO H,Okl dudng riidng

vudng gdc vdi AB cdt nda ,^ ,

Hin cuo dudng Hdn (O) Idn

luqt Iql C vd D. Ta ed:

C H » ^(»-IX3-l)SOfl=.2 =(>ft^+^ ^ S4=»

V*^-i->/3-jS2 . Ddu bdng xdy ra khi vd chf khi

x-2 .

Cddl 7: Xll hdm sd y - J7^+S^ vdt

•Hudng )(«> dyng dllu kl|ncd nghllm cOa

mdl phuang Hinh (PT) bdc hai): Gqi T Id Idp gid

HIeOahdmsdyvd y,£T^y,=4ir-i+^li^.

PT y,.4ii^*-l3^ cd nghllm i6[y]

**|>.'-2.2V(»-lX3-x) ^|i'-4»*3*ioi-2)'-»

- Hudng 2 (sd dyng dilu ki|n ed nghi|m ciio

h| PT ddl xOng): Ta Hm yj dl PT y, = V;r^+. ^

cd nghllm. Ddl u = 4x^'i -Ji-x, vdi iiaO,vso,

(ll + v=v [•'*'>'>,

ta duqc h| FT j.'+,.J2 ° Vv.io..'-2)- HI PT

* Mi l TIPT aq«l nil Ctal - M Tih Guv

Tjp Chi BIto dye s6 291 on i . I/MMI