BOI DUONG NANG LlTC PHAT HIEN UA GIAI QUVET UAN DE • • CHO HOC SINH TRUNG HOC PHO THONG QUA DAY HOC GIAI PHUUNG TRiNH VA HE PHU''''ONG TRINH O ThS L^ TRUNG TIN'''' Trong day hoc mon Toan luon doi hoi nguai[.]
BOI DUONG NANG LlTC PHAT HIEN UA GIAI QUVET UAN DE • • CHO HOC SINH TRUNG HOC PHO THONG QUA DAY HOC GIAI PHUUNG TRiNH VA HE PHU'ONG TRINH O rong day hoc mon Toan luon doi hoi nguai T ThS L^ TRUNG TIN' Vi dy 1: Tim m de PT: mx^ - (m - 4)x + m = (1) hoc phdi CO tir sang tqo, nhqy ben va linh hoqt Co rat nhieu each djnh nghTa ve dqy hqc phdt hien j P H ) vd gidi quyet van de (GQVD), song c6 the hieu: dqy hqc PH vd GQVD Id qud trinh dqy hoc dd gido vien (GV) to' chuc cho HS duoc hoc tdp tronq hoat donq vd li r Jd • ' ^^ L L -' J bang hoqt dqng thong qua cac tmh huong dqy hoc md GV dua ra; cdc tinh huong ndy HS chua gidi d d p duqc nhd mqt thuqt gidi nhung cd the lien he vdi nhCrng kien thuc dd biet vd cd khd ndng vuot qua neu cdc em tich cue suy nghT, hoqt dqng de bien dd'i doi tuqng hodc dieu chinh tri thuc dd cd Cd the chia qud trinh dqy hqc todn theo hudng PH vd G Q V D thdnh buoc sou 1) PH van dS: GV dua tinh hudng hqc tdp de HS PH vdn de, sou dd gidi thfch, chinh xdc hda vd phdt bieu vdn de; 2) Dgt myc tieu: GV to chuc cho HS quan sdt, phdn tfch ldm rd cdc van de vd ddt myc tieu G Q V D ; 3) Tim cdch gidi va lap ke hoach gidi: Ddy Id budc quan nhdt tie'n trinh gidi todn GV huong ddn HS khdi qudj c6 hai nghiem x,, x^ thoa man: -1 < x, < x^ 1) GV yeu cau HS neu each gidi bdi todn: 77m j;$^j kien cdn vd du de PT cd hal nghiem duong p/,^^ £,y^^ ^S suy nghi vd trd loi duoc: Di4u kien cdn vd du 4.,„ j , n ^ L'• LJ Lde PT o x ' + b.x + c = CO nai nghiem duong phan ^ " ° "^ y.^ \Qa^O; A^O;VQ S = — >0 yd P = ->0 a a Sou dd, GV neu bdi todn: Tim m de PT (1) c6 hai nghiem x,; x^ thda mdn -1 < x, < Xj 2) De PT (1) cd hai nghiem phdn biet x,, x^, d i l u kien cdn vd du Id: m ^ vd A ' = - G m ^ - S m bdi tcjdn theo n h i l u gdc dq khde nhau, HS co t h l vdn dyng cdc thao tdc tu nhu: khdi qudt hda, ,^5 ^g dqc biet hda, tuong tu hda de dua ro cdc hudng GQVD, sou dd lua chon cdch gidi hay nhd't; ; r / „ / c / / e n cdc i>(A7c G Q V D : GV eho HS trinh Hudng gidi thu hai: To thd'y u' ^o"^ |x jt^>o ' ^ , , „ • , i \, i.V 4-.' ^ V dqt cau hoi, lieu rang phep b.en doi bdy cdch gidl d l G Q V D ; 5) Kidm tra: HS k i l m tra cdc buoc G Q V D dudi su gidm sdt cua GV, sou dd tim them cdc cdch gidi khde; 6) Vdn dyng vd md rdng vd'n d l : GV hudng dan HS dua U >-i k+x, >-u(-i) , ^^ U > - ' U ^ >(-')(-') ^ ^ ^ ' chi cho HS thd'y soi ldm ldp ludn ndy Hudng gidi thu ba: Tu d i l u k i e n ung dyng cua cdc ke't qud (ne'u ed), m d r o n g , tong quat hoa van d e , d e xuat van de moi Dudi ddy, chung toi trmh bay mqt so tmh hud'ng day hoc giup HS trung hoc phd' thdng bdi dudng ndng luc PH vd G Q V D dqy hqc gidi ^ r( i)^(,^ + ,)>0 U+x,>-2 ^ \ ^^ir+r+rr^ ' ^\ ^\' , ^ , , ^^ ^ GV hudng dan HS chuyen bdi toan ban ddu ve viec tim m 6e PT dd cho cd hai nghiem phdn biet cdc bdi todn v l PT vd he PT * Tnrdng THPT Chuyen Nguyfen Hue • Ha Noi Tap chi Giao due so (kn • 10/2011) + 16 hay - < /ô < ^ (ã) d i l u ndy HS cd the' tu suy ludn duqc Myc tieu dqt Id: tim m thda mdn dieu kien (•) ^e x > -1 vd x , > - jj ^ ^ ^ ^ ^ ^,-^,- ^/,^ „/,5> - p ^ ^ j | ^ , » - - V - ^ ' - m i ^ _ , ^^ ,.'"-4W-3.'-8 6^_,^ - 1^.^ ^ ^ ^^ bd't PT rd't ph^c tap ^^^ X,; x^ thda man Xi + Xj > - Trong ba hudng gidi tren thi hudng gidi thu ba Id phu hqp nhdt 4) HS trinh bdy Idi gidi: De PT (1) ed hai nghiem phdn bidt x,, X2, d i l u kidn cdn vd du Id ) < m < % d m ^ Khi dd, theo dinh li Vi-et, ta m-4 co: K O Dodd: m>— i kit hop vdi dieu kien (*), ta duqc: -4 < m < 5) GV yeu cdu HS kiem tra Iqi ede budre gidi bdi todn, sou dd hudng dan HS su dyng thi hdm bdc hai d l gidi bdi todn theo mdt cdch khde vd rut nhdn xet: De PT: f(x) = ax^ + bx + c = cd hai nghiem x,, x^thda mdn -1< x, < x^, dilu kien edn vd du Id: a ?t 0; A > 0; o.f (-1) > vd T ^ ~' Ngodi ra, GV cd t h l huong dan HS tim mqt cdch gidi nua bdng phuong phdp hdm so nhu sou: Tu PT: mx^ (m - ) x + m = /" = -4x | ' j : ' - y - t ^ v + -vv'=0(l) , , duqc PT: F 2F + f - = 0, HS gidi duqc t = 2, suy X = 2y Vi dy 3: Gidi PT: 2x' +4 = 5sf77l(]) 1) GV yeu cdu HS neu each gidi phuong trinh: 4x-5 = >j2x^+ \, sou dd GV yeu cdu HS tim cdch gidi PT dd cho 2) Nlu binh phuong hai ve eua phuong trinh (1) ta se duoc mdt PT bqc khdng ed nghiem huu ti Vi vdy, bdi todn cdn gidi theo mdt cdch khde 3) Vai dilu kien x > - l , ta cd the viet Iqi PT dd cho thdnh: 2.{x'-x + \ + x^\)= sjix + \u.x' -x+\) 2(y]{x^-x + \f ^^ix + \f)= 5V(x + l).(x^-x + l) Neu ddt u = yjx^ - X +1; V = Jx + ] ta thu duoe mqt PT dd biet cdch gidi: 2(t/ + v^) = 5uv 4) GV yeu cdu HS trinh bdy cdch gidi 5) HS cd t h l gidi PT bdng cdch phdn h'ch: PT (2>/x'-jt + l - v ^ ) ( V r - - x * l - > / J r T T ) = 6) HS rut nhqn xet ve cdch gidi PT dqng: tren khodng (-1, + 00), tim dilu kien d l dudng thdng y = m cdt dd thj hdm so y = g(x) tqi hai dilm phdn biet ed hodnh Idn hon 6) GV cho HS rut cdch gidi bdi todn tong qudt sou: Vdi sd thue a cho trudc, tim dieu kien de PT: f(x) = ax^ + bx + c = Qcd hai nghiem x,, x^ thda oa mt man a