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TAO Mm THU CHO HOG SINH THONG QOA CAC DAI TOAN v i BAT DAriQ THUC (TOAn 10) I Trong giang day, phat huy tinh tich ci/c cua HS Iadieu quan trpng nhatcua noi dung doi m6i phuang phap De lam datfcdieu na[.]
TAO Mm THU CHO HOG SINH THONG QOA CAC DAI TOAN v i BAT DAriQ THUC (TOAn 10) ThS I.Trong giang day, phat huy tinh tich ci/c cua HS Iadieu quan trpng nhatcua noi dung doi m6i phuang phap De lam datfcdieu nay, moi giao vien (GV) can dau tir thdi gian,lu6n tim toi vaphathien nhi/ng vande m6i, tur hiding HS den vdi "the gidi rang md' cua loan hpc, lihol day long dam me toan hpc dcac em Trong qua Irinh day hpc, chung toi lhay cd nhiing bai tap nhin qua tirdng chi)ng nhir rat don gian, nhung neu chju kho tim hieu Ihi se kham pha dirpc nhieu dieu thu vjtdnhirng bai toan dd Bai viet chung toi trao doi cung dong nghiep va dpe gia mpt so'bai toan ve bat ding IhiJc (BBT) chuang Irinh toan hpc Idp 10 BBT la mpt phan quan trpng chuong Irinh Toan phd'thdng, nd ludn dUdc decap den Irong cac ki thi HS gidiva cac ki thituyen sinhdai hpc Tuy nhien, day la mpt mang khd vi vay da so' HS thudng bd qua c&u GV phai iam de HS tie'p thu dupc kien thi^c vephan mpt each chu dpng,tl/ dd cac em hiing thu hon hpc Toan Be nang cao ttiu hpc tap men Toancho HS, Ihdng thudng sau khlHS lam xpng mpt bai toan nao dd, GV can dat cho HS cac cSu hdi sau:-Lieu bai toan cd trudng hpp rieng nao khdng?; - Cdthetd'ng quat baitoan dupc khdng?; - Cd the ap dijng bai toan de giai cac bai toan khac dudc khdng? Chinh nhi?ng cau hoi lam cac em phai suy nghlva Cling vdi suhudng d i n cua GV cac em cdthe tim duoc cau tra idi T i i dd, cac em yeu Ihich hpc mdn roi/rhon Vidu, baitoan: Chiing minh ring neu LE Q U A N G H A O ' - Chiing minh ring ne'u a, b, c ia ba sd duong thi - Chiing minh ring nd'u a, i> ia hai sd duong Ihi I M ( " + ' ) : ^ + ^ ^ 4, Khi nao xay dang thiic? - Chiing minh ring ne'u a, b la hai sd duong thi 1 , ' - + T ^ — Khi nao xay dang thdc? a b a+b ' ^ • Chiing ring neu a,, a^ a„ iacac sdduong thi (o,+a,+ +o.) — + — + + — > n ' K h i n a o xayra ding thiic? Tao hixng thu cho HS qua khai thac "bai toan gd'c" 1) Bai toan goc Bang nhiing kinh nghiem thi/c tien giang day, GV cd the chpn cac bai toan SGK cd tinh khai quat cao (tuong dd'i) iam "bai toan gd'c" Ve BDT (Dai sd'10), chung tdi chpn "bai tpan gd'c": 1) Chiing minh ring neu a ^ va > ttii a ' + i ' > a i ( a + i ) ( b a i , t r 110-OaisolOnangcao) Chung minh:BDTtuong duong (o+*)(a^-2ii*+(>^) o (o+6)(a-6)^ >o BDT dung, da'u "="xay va chi khia = d a, b, c i a b a s ' d u a n g l h i C ' ' + ' + c ) ( - + ^ + - | s ^ Khi nao xayra d i n g thiic? Viec chiing minh baitoan kha don gian, sau MS chiing minh xong, GV nen dat cau hoi: • BDT Iren tuong duong BDT nao?; - Neu xet vdi hai sfiduong thi ta cd BDT nao?; - Lieu bai loan cd diing cho nsd'duong khdng? Tilcac cau hdi Iren, da giiip cac em lim dupc cac BDT cd nhieu ting dung viec giai cac bai toan cac ki thi tuyen sinh dai hpc nhiing nam gan day: (ki2-8/2014) 2) Chiing minh rang vdi hai sd thuc a , dtuyytacd: a*+b*>a^b+ab^ (dai 7b, tr 110 - Dai so 10 nang cao) Chiing minh baitoan tuong ti/bai Sau chiing minh xong hai bai loan neu tren, GV can gpi y cho HS khai thac t?o thu qua giai bai loan va bai 7b nhusau: 2) Tao thu hgc toan qua "bai loan goc" - Hudng khaithae dan gian: N eu chii y, bai toan va bai 7b cd the tong quat nhu sau: * Tnriing THPT Chuyen Huynh Man Dat tinh Kien Giang Tap chi Gide due so 340 51 + Bai6.1 Chung mmh r§ng neu a > va > thi: ^2n+i ^^2n+i > ^2n£,^^^2n {yoj n nguyen, di/cfng} Thatvay, BDTtaang duang (a^"-6^")(a-fe)>0, BDT dung, dau "=" xay va chi a = b Den day, neu ta ap dung cong friuc sm'« = u cos' a ta duoc bai toan 6.6 + Bai 6.6 Cho tam giae ABC Chung minh rang: £2{sin/* + + Bai 7b.1 ChiJng minh rang vo'i hai so thi/c a, b y, ta c6: a^" + fp-" > a^"-^b+a6^""' (vert n nguyen, du"cfng) mC)^ Chung minh tUtfng tubai6.1 Neu xuat phat tur bai 7b.1 vert /? = / ta co BDT quen Tuket qua tren, luu y HS giai mgt bai toan nao ta CO the chu y den cac tnj'dng hffp rieng (neu co) thupc o^ + 6' > 2ab vdi moi a,/jthupc R; vert /7=2ta co hoac ta co the tong quat hoa bai toan bai toan 7.b.2: a'^+b'* >a^b-i-ab^ (1) vcri mpi a, b - Hudng khai thac muc ning cao: Neu v6i a>0,b>0, Ll thupc R;neu ta thay boi gl vdi a ^0, b ^0 (1) c>0{Xilba\^.^){a CO ^+—>a+b, -i b tuong duong ^ j ^ ^ ab xuang \\sXac6-T^^ be, J "^ " a+b • b +c^ V ^ s ^c Cong cac BDT Iren ta co bai toan7b,2 c +a + Bai 7b.2 Cho a, b, e la cac so thue 5^0, Chung minh r^ng: a — + ^ > c + , —+—>a+c Cong cac BDT tren C b c a • ^ ta CO bat toan 6.2 + Bai 6.2 Cho a, b, c\a ba soducfng Chung minh rang:_ b^ +a^ >2(a + b + c) a''+b^ V+c"* a^+b^ 6^+c^ j-tab c' +0' + bc+ca yd\n = Xa co BDT a* +b^ > a^b+ab^ (2) vdi mpi Bai toan 6,2 tuong dUdng a, b thupc R, Tuong l u nhu tren la co bai toan 7b.3 a\]- + -) + b\- + -) + c\]- + -)>2{a + b + c) DC a c b a a \ ^ ) + b\^^) ' be « + c = 1, ta co: a\^)+b\^-^)+cH^)>2 be ac « ab o'(i-a)+6^(i-z>)+c^{i-c)>2i76(?.Dendaytac6bai toan 6.3 + Bai 6.3 Cho a, b, c la cac so duong thoa man a+d+c=1.Chijngminh:fl'+6'+c'>a' + 6'+c' + 2aAc Neutadata= / j , b = ^ , c = i/^.Talaic6them baitoan 6.4 + Bai 6.4 Cho x,y, z laba so duong thoa man Z'-Z ^ , Neu ta coi a, b, c la dai ba canh cua mot tam giae thi tu'6.2 kel hop djnh li sin ta c6 bai toan: •f Bai 8.5 Cho tam giae ABC Chung minh r^ng: sin^.^ + sin^ B sin^fi + sin^C sinC sin A 2{sinA+sinB-h sinC) s'm^C + sin^ A sinB + Bai7b.3.Choa, 6, clacaesolhLrc^O.Chiing minh r&ng: + c\^)>2{a + b + c).Qala+b ,,1-A, ,1i,l-c, a'' + b'' b''+c'' rtab + bc + ca a''+b'* b'' + c'' lis bai 7b.2 va bai 7b.3, tong quat bai toan 7b.4 + Bai 7.4 Cho a, b,c\a eae so thi/e ?iO Chung minh ring: Jh'*l.L2^*2 L2«*1 , „2B+2 a" +b b " +c (vdi/T nguyen,duong) 2ôt2 , 2iit2 ã +-T:>flO+f>c + cfl c"' +a"' Tai li|u tham khSo NguySn Huy Doan (chu bien) Dai stf 10 (nang cao) NXB Gido due E 2006 Tr^n Van H90 (tdng chu bifin) D^i stf 10 NXB Gidodfic, H.2001 SUMMARY In teaching, improving students activeness is the most important thing when we want to renovate our methods To make it work, each of us, teachers, must spend a lot of time studying and discovering new things As a result, we can lead our students to the new open horizon, making them more interested in our subject Through my teaching period notice that some exercises seem to be simple However when we try our best to solve them, we can get many interesting and surprising from them 52 Tap chi Giae due so 340 (kl2-8/2014) ... quen Tuket qua tren, luu y HS giai mgt bai toan nao ta CO the chu y den cac tnj''dng hffp rieng (neu co) thupc o^ + 6'' > 2ab vdi moi a,/jthupc R; vert /7=2ta co hoac ta co the tong quat hoa bai... bai toan7b,2 c +a + Bai 7b.2 Cho a, b, e la cac so thue 5^0, Chung minh r^ng: a — + ^ > c + , —+—>a+c Cong cac BDT tren C b c a • ^ ta CO bat toan 6.2 + Bai 6.2 Cho a, b, c\a ba soducfng Chung... o''(i-a)+6^(i-z>)+c^{i-c)>2i76(?.Dendaytac6bai toan 6.3 + Bai 6.3 Cho a, b, c la cac so duong thoa man a+d+c=1.Chijngminh:fl''+6''+c''>a'' + 6''+c'' + 2aAc Neutadata= / j , b = ^ , c = i/^.Talaic6them baitoan 6.4 + Bai 6.4 Cho x,y, z laba so duong