TRAN VINH rturso TAP HAI 10 // -2 -1 NHA XUAT BAN HA NOI TRAN VINH THIET KE BAI GIANG j^" [)AI SO NANG CAO - TAP HAI NHA XUAT BAN HA NOI CbirdNq IV BAT DANG THlTC VA BAT PHl/OlNC TRINH PHAN1 I NOI DUNG Ndi dung chinh cua chuong IV : Bat phuong trinh : Bat ding thiic ; Dai cuong ve bat phuong trinh ; Bat phuong trinh va he bat phuong trinh mdt an; Dau cua nhi thiic bae nhat ; Bat phuong trinh va he bat phuong trinh bae nha't hai dn; Dau cua tam thiic bae hai; Bat phirong trinh bae hai; Mdt sd phuong trinh va bat phuong trinh quy ve bae hai B a t d a n g thaiti On tap ve khai niem bat dang thiic; Bat dang thuc ve trung binh cdng va trung binh nhan (bat ding thiic Cd - si); Bat dang thiic chiia gia tri tuyet ddi Ndi dung chinh cua phan la xay dung quan he thii tu tren tap hgp sd thuc Sach trinh bay mdt each het siic co ban, he thdng ve bat ding thiic Trong phan ciing dua cac tinh chat, quy tdc ve bat ding thiic, tir dd giiip hgc sinh chiing minh dugc cac bat ding thuc don gian Dac biet phan cd dua vao hai bat ding thiic : Bat ding thiic v6 trung binh cdng va trung binh nhan; bat ding thiic cd gia tri tuyet ddi B a t p]» b" "a > b" "a < b" dugc ggi la nhiing bdt ddng thdc Hoat ddng cua GV Cau hoi Dien vao chd trd'ng: a < b c ^ a - b < a-b0 Noi dung a >b>0=> a" b" a < b yla ^b a < b c^ yfa yfb Nang hai ve ciia bat ding thiic len mot luy thira Khai can hai ve cua mdt bat ding thiic Nhom Dien => hoac c^ vao chS trdng Tinh chdt Dieu kien Ten goi Noi dung a + 2V7 (c) m G ; (d)m Trd Idi Chgn (d) 11 Nghiem cua ba't phuong trinh x(x + 4) < (x^ + 2) la (a) X < hoac x > 4; (c) X < 4; (b) X < - ; (d) X > i2 Trd lai Chgn (b) 12 Nghiem ciia bat phuang trinh 2(x+l)^-43>3xla 166 (b) m < -2 + 2V7 -2+2V7 2+2V7 (a) X > -2; (b) X < 4; (c) X e ; (d) X e M Trd Idi Chgn (c) 13 Nghiem cua bat phuang trinh 2x + , la < X -5x + x-1 (a)S = ( - ^ ; l ) ; (b) S = (9;+c»); (c)S = ( l ; ) u ( ; + a ) ) ; (d)S = (4;9) Trd Idi Chgn (c) 14 Nghiem cua bat phuong trinh x^-6x + x^+6x + x - , la x+ (a)x — ; 10 (c)x>0; (d)x € (-o); l ) u V -5; Tra/^/ Chgn (d) 15 Tap xac dinh cua ham sd f(x) = (a) (-o); 0); (b) (-c»; -2); (c) (-2; 0); (d) R 1-x - la X +X + Trd Idi Chgn (c) , [ x ' - x + < ^.„ ,^ 16 He bat phuong trinh vo nghiem [x + m > (a)m< 1; (b) m > 4; 167 (c)m>l; (d)m x - hay x - < Cau hdi Hay giai bat phuang trinh: —X— >—X Vay 23 x< — Cau hdi Giai Ggi y tra Idi cau hdi Bat phuang trinh da cho tuong duang bat m x + >m phuang trinh -x vdi (m +l)x>m x> Cau hdi De he cd nghiem cin didu kien gi? - hay m4 - 11 m^-l m^ +1 Ggi y tra Idi cau hdi 23 w -1 < — Ddp so' \m\< 5V2 169 Bai 80 Hoat ddng cua HS Hoat ddng cua GV Ggi y tra Idi cau hdi Cau hdi Hay dua bat phuang trinh vd Bat phuang trinh da cho tuong duong dang ax + b>0 vdi: (m^ +m + \)x + 3m + \>0 Ggi y tra Idi cau hdi Bat phuang trinh da cho cd nghiem la Cau hdi Tim nghiem cua bat phuang -3w-l trinh ^- m +m + \ Ggi y tra Idi cau hdi ^^, - m - , , ^ > -1 hay < m < Khi -^ Cau hdi m +OT + Bat phuang trinh da cho nghiem diing vdi mgi x e [ - ; 2] nao? Bai 81 GV chiia cau a) 'Hoat ddng cua GV Hoat ddng cua HS Cau hdi Ggi y tra Idi cau hdi Hay Tinh A A= -l(m-\)(m + l) Cau hdi Ggi y tra Idi cau hdi Hay bien luan bat phuang Ne'u A < m < -7 trinh da cho phuang trinh nghiem hoac m > 1, bat diing vdi moi X G M Neu -7 < m < A > ba't phuong trinh cd tap nghiem la mdt khoang GV tu vie't khoang nghiem 170 a) Hudng ddn Bat phuang trinh cd dang: (a^ -3a + 2)>2 Tit dd dua each bien luan bat phuang trinh Bai 82 GV chiia cau b) Hoat ddng cua GV Hoat ddng cua HS Cau hdi Ggi y tra Idi cau hdi Hay dua bat phuang trinh ve Bat phuong trinh cd dang: dang: '^^''^>0 • Qix) x^-3x + Cau hdi Ggi y tra Idi cau hdi Hay lap bang xet da'u va vie't Tap nghiem ciia bat phuang trinh: tap nghiem cua bat phuang ( - o ) ; l ) u ( ; ] L J [ ; + a)) trinh a) Hudng ddn Lap bang xet dau va dua tap nghiem S = i2;4)Kj(5; + cc) Bai 83 GV chiia cau a) Hoat ddng ciia GV Hoat ddng cua HS Ggi y tra Idi cau hdi Cau hdi Hay viet bat phuang trinh Khi m= 4, bat phuang trinh cd dang: m = 2m - < Bat phuong trinh khdng cd Cau hdi nghiem vdi moi x G R Hay neu dieu kien de bat Ggi y tra Idi cau hdi phuang trinh cd nghiem vdi fA Cau hdi Ggi y tra Idi cau hdi Hay giai bat phuang trinh Bat phuang trinh da cho tuong duang vdi rx>4 [x-7 Cdu (2 d) Bat phuang trinh x - 4x + < cd tap nghiem la [ 1; ] 3m Bat phuang trinh 2x - 3m > cd nghiem la x > — De bat phuang trinh cd nghiem la mdt doan thi 3w , , < hay m < — Cdu (2d) a) X -1 ; 5-17 u + V17 ;+Go ^jxG ( - o o ; - l ) u ( ;2) 179 [...]... minh 1 k(k + 1) 1 k 1 k +1 H2 Tinh tong ^ + - L + - i - + + ^ 1. 2 2.3 3.4 1 n(n + l) H3 Chung m i n h - ^ + - ^ +-• + + ^ a -K a Va e :i: 18 (b) a"^ + 1 < a'' -h a Va G J 1 V a (d) a^ + 1 = - Va 2 Tra lai (c) a 1 11 Cho — < - (vdi b > 0) hay chon ket qua dung trong cac ket qua sau b 2 ^ a +1 1 (a) < b 2 ^ a +1 1 < (c) b+2 2 Tra Idi (c) .u^ a + 1 1 (b) < b... - 1 > 0 Vx; (b) x^ + x + 1 > 0 Vx; (c) - x ' + X + 1 > 0 Vx; (d) x^ - X - 1 > 0 Vx Trd Idi (b) 15 Chgn ket qua diing trong cac ket qua sau (a)x^+lOVx; (c) x^ - X + 1 = 0 Vx; (d) x^ - X + 1 = 0 tai X nao dd Trd Idi (b) 16 Chgn ket qua diing trong cac ket qua sau 1 2 (a) 0 < a < 1 thi - < ; a a +1 1 2 (c) 0 < a < 1 thi - = ; a a +1 Trd Idi (b) 1 2 (b) 0 < a < 1 thi - > ; a a +1 1 1. .. .u^ a + 1 1 (b) < b 2 a a D (b) |a| - 1 < |a + l| Tra Idi Cau (a) (b) (c) (d) Dien D S D D 13 Hay chgn ket luan dung trong cac ke't qua sau (a) |x| < l 2 Thuc hien H2 GV cho HS doc va hieu noi dung H2 GV treo hinh 4 .1 Sau do thuc hien theo cac thao tac sau: GS-^ thao tdc trong 3 phiit Hoat dong cua GV Cau hoi 1 Hay xac dinh gdc ACB Cau hdi 2 Hay tinh OD Cau hdi 3 Hay tinh CH Cau hdi 4 Hay so sanh OD va CH, tCr dd riit ra bat dang thiic Hoat dong cua HS Ggi y tra 16 1 cau hdi 1 ACB =90° Ggi y tra 16 1 cau hdi 2 0D=^+^ 2 Ggi y tra 16 1 cau hoi... tren (ke ca |H1| bing HD sau) 10 Hoat dong cua H S Hoat dong cua G V Cau hoi 1 Hay chiing minh bat dang thiic : \a + b\< \a\ + \b\ bang each binh phirang hai ve Ggi y tra 16 1 cau hoi 1 \a + b\ < \a\ + \b\ c^ (a + b)^ < a^ + 2\ab\ + b^ a^ + 2ab + b^ < a^ + 2\ab\ + b^ o Cau hoi 2 Hay chimg minh bat dang thiic : \a\ - \b\ ... 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