EBOOK bài tập đại số 10 NÂNG CAO PHẦN 2 NGUYỄN HUY ĐOAN (CHỦ BIÊN)

phucmg IV BAT DANG THl/C VA BAT PHaONG TRJNH A NHONG KIEN THQC CAN NHO Tinh chat cua bat dang thurc l)a>bvab>c=>a>c 2)a>boa + c>b + c 3) Ne'u c> thi a > b '^ ac> be Ne'u c < thi a > b ac < be Cdc he qua 4)a>bvac>d=>a a + c>b a>b- + c>b + d c 5)a>b>0vac>d>0=^ac>bd 6) a > ^ > va n G N* => a" > &" l)a>b>0=>Ja>^fb S)a>b=>^>^2 Bat dang thiirc ve gia trj tuyet doi Ddi vdi hai sd a, b y, ta cd ^ Id - \b\ , /7 > , t a e d a + b ^ i—r a + b r-r ^ > y/ab ; ^ = ^Jab 0, b>0,c >0,taed a + b + c ^ 3r-r- a + b + c ->/—— r > y/abc ; ~ = yjabc a = b = c Ap dung 1) Ne'u hai sd duong cd t6ng khdng doi thi tich cua ehiing Idn nha't hai sd dd bang 2) Ne'u hai sd duong cd tich khdng ddi thi tdng ciia chiing nhd nha't hai sd dd bang Bie'n doi tUdng duang cac bat phudng trinh Cho ba't phuong trinh fix) < gix) cd tap xac dinh ®, y = hix) la mdt ham sd xac dinh tren y^ Khi dd, tren 2), ba't phuong trinh fix) < gix) tuong duong vdi mdi ba't phuong trinh 1) fix) + hix) < gix) + hix) ; 2) fix)hix) < gix)hix) ndu hix) > vdi mpi x e S); 3) fix)hix) > gix)hix) ndu hix) < vdi mpi x e 3) Bat phUdng trinh va he bat phuong trinh bcic nhat mdt an • Giai va bien luan ba't phuong trinh ax + b thi niia mat phang (khdng kd bd id)) khdng ehda didm M la midn nghiem ciia (1) ^ 9 Chii y Ddi vdi bat phuong trinh ax + by + c X2) Ndi each khae, « / U ) < X e (x^ ; -^2)' afix) > O X > XT \a>0 J 2) \/x s R, ax + bx + c> c^ X < Xj [A < a \a ft thi — > ft ft + c a c 4.4 Cho «, ft, c, d la bdn sd duong va — < — Chdng minh rang : , a +b c +d a) — r — < — — , , (3 + ft f + J b) > 4.5 Cho ft, ti la hai sd duong va — < — Chihig minh rang a 'b^ a +c c b + d'^'d' 4.6 Cho a, ft, c, d la bdn sd duong Chiing minh rang 1< a b e d ~ 4.24 Cho a, ft, c la ba sd duong Tim gia tri- nho nha't ciia A= a b c ft + c + c + a + a + b 4.25 Trdn mat phing toa dp Oxy, ve dudng tron tam cd ban ki'nh R iR> 0) Tren cae tia Ox va Oy l^n lupt la'y hai didm A va B cho dudng thing AB ludn tie'p xiic vdi dudng tron dd Hay xae dinh toa dp eiia A va dd tam giac OAB cd dien tich nhd nha't 105 §2 DAI C i r O N G Vfi B A T PHLfONG TRINH 4.26 Trong eac menh dd sau, menh dd nao diing, menh dd nao sai, vi ? a) la mdt nghiem ciia ba't phuong trinh x^ + x + > b) - khdng la nghiem cua ba't phuong trinh x^ - 3x - < c) a la mdt nghiem ciia ba't phuong trinh x + (1 + a)x - a + < 4.27 Cac cap ba't phuong trinh sau cd tuong duong khdng, vi ? a) 2x - > va 2x - + x-2 > X- ' b) 2x - > va 2x - + ——- > x+2 x+2 ' c) X - < va x^(x - 3) < ; d) x - > va x^(x - 3) > ; e) X - > va (x - 2)^ > ; g) x - > va (x - 5)(x^ - 2x + 2) > 4.28, Tim didu kien xac dinh roi suy tap nghiem cua mdi bat phuong trinh sau : a) V x - > V - X ; b) V2x - < + V2x - ; e) d)3x+^—>2+ x-2 -^ six-3 < ^ ; Vx-3 ' ^ x-2 4.29 Khong giai bat phuong trinh hay giai thi'eh tai cac bat phuong trinh sau vo nghiem : a) V ^ + < ; b) (x - 1)^ + x^ < -3 ; e) x^ + (x - 3)^ + > (x - 3)^ + X- + ; d) Vl + 2(x + l)^ + > / l - x + x^ < 4.30 Khong giai bat phuong trinh, hay giai thich tai cae ba't phuong trinh sau nghiem diing vdi mpi x : a) ,v* + x^ + > ; c) X^ + (X - 1)^ + — > x^ X- + 106 b) ^^^f^ > ; x^ + 4.31 Tim didu kien xdc dinh ciia cac ba't phuong trinh sau : 1 ^ ' • a) (X +1)2T + X - n > ;' ^^ v G m 1 b) VTTT , + (X - — — > 2)(x - 3) x-4 4.32 Di giai baj: phuong trinh Vx - > V2x - (1), ban Nam da lam nhu sau : Do hai ve' eiia ba^t phuong trinh (1) luon khong am nen (1) tuong duong vdi (Vx-2)2 > (V2x - 3)2 hay X - > 2x - Do dd X < vay tap nghiem ciia (1) la (-QO, 1) Theo em, ban Nam giai da dung chua, vi ? 4.33 Ban Minh giai ba't phuong trinh , < (1) nhu sau : Vx2-2x-3 '^ + (l)x + 5< Vx^ - 2x - (X + 5)2 < x^ - 2x - 12x + 28 ; d) ^2x - - V x - l > 107 4.36 Giai cac he bit phuong trinh sau va bidu didn tap nghiem tren true sd : 3x + - < X + a) 6x-3 b) < 2x + 1; 4x + < 2x + > X - 7x - 4.37 Giai va bien luan cac bat phuong trinh (in x): a) mix -m)>0 ; b)(x- l)m>x + 2; ^ X - ab X - ac x - be + x + l Chia hai ve eho Vx + > , ta ed Vx - - > Vx + Vi X > nen Vx - < Vx + 1, dd V x - l - < Vx + vay ba't phuong trinh (1) vd nghiem Theo em, ban Nam giai diing hay sai, vi ? 4.39 Tim cac gia tri ciia m dd he bit phuong trinh sau ed nghiem : Ix + 4m^ < 2mx + l3x + > x - I 4.40 Tim cae gia tri eua m de he bat phuong trtnh sau vd nghiem : \mx + | + |c| = i\a\ + \b\) + \c\ > |a + 6| + |c| > |a + ft + cj Dang thuc a 0, > 0, c > hoac |x + + x + + - x | = Dang thdc xay ra, chang ban tai x = Vay gia tri nho nhdt ciia/(x) la 18 a) Vdi a > 0, & > 0, c > ta ed ac + — > 2.\ac.— = c \ c 24ab b Dang thiie xay ac = — hay b = ac c ,\ a b ^ ab ^Arr b) -= + -==> 2, - p = - 2ylab sib 7a \ylab Dang thiic xay a = b 19 b) X + ^ ^ = X- 2+- ^ + > 2^(x - 2)—^ + ^ (vi x - > 0) Dang thiic xay x = v a y gia tri nho nhdt ciia ^(x) la 251 20 a) Cdch I TiX ddng thiic (a^ +b^ +e^)ix^ + y^ + z^) = = iax + by + czf + iay - bxf + ibz - cyf + iaz - ex)^ de dang suy (a^ +b'^ + c^)(x^ + y^ + z^)>iax + by + czf ay = bx t a b e bz = ey tuc la — = — = — X y z az = ex Dang thiie xay Cdch 2 2 2 2 (ax + by + ez) = a x + b y + c z + 2abxy + 2acxz + 2bcyz < ^2_^2 ^ ^2^2 ^ ^2^2 ^ ^2^2 ^ ^ ^ ^ ^2^,2 ^ ^2^2 ^ ^2^2 ^ ^2^2 = (a^ +b^ +c^)(x2 + y^ + z^) b) (x + 2y + 3z)^ ^i\.x + 42.42y + S.Szf < (x^ + 2y^ + 32^)(1 + + 3) = 6.6 - 36 Vi vay |x + 2y + 3z| < 'x + < 2x - 21 a) I > x +3 x>4 X Vay tap nghiem S = (-oo ; -2,8) u (0 ; +oo) b) -5 10 < Tam thdc ludn duong va chi A = -(llm^ + 2m + 11) < —;— ^ b) Vdi m = - - , dd bidu thirc cd gia tri la - - > 0, dd m = - khong thoa man Vdi m i= - - ' dd bidu thiic da cho la mpt tam thiic bac hai 255 Tam thdc ludn am va chi [a = 5m + < |A 28 o m 0, suy tap nghiem la (-4 ; 0) u (0 ; +^) b) Bat phuong trinh dupe bie'n doi tuong duong vdi x'+l6 >0 x ^ ( x - ) ( x + 2)2 Suy tap nghiem la S ^ (2 ; +co) 29 a)63 - m 3 < 20 -x^ + 4x - > b) S = -I-' Gai y Ba't phuong trinh tuong duong vdi : x + l0 v • V fn v-r V2 Gai y Dat t = 72x^ - > b)5 = (-oo ; - l ) w ( ; + cx)) Gm y Dat f = 7x^ - 3x + > 36 a) Da'u hieu la tudi cac ba me d nude MT sinh l^n dau Don vi didu tra la cac ba me d nude Mi sinh eon lin diu b) Tudi trung binh la 22,89 c) Bang phan bd tan sua't 258 Khoang Tin sua't(%) [15 ; 19] 31,6 [20 ; 24] 35,5 [25 ; 29] 19,8 [30 ; 34] 9,6 [35 ; 39] 3,5 d) Bidu hinh quat (h.5) e) Bidu dd tan suat hinh cdt (h 6) 40 • • •• 20 • -rmm 10- n 15 19 20 Hinh 37 24 25 29 30 34 35 IX 39 Hinh Gpi sd be nhat la a Sd Idn nhat la a + 18 > Vay cd thd xay hai trudng hpp sau Trudng hap J Mau l a a ; & ; ; ; a + 18 (sap xe'p theo thii tu tang din) Khi dd tong eae sd lieu \a2a + b + 34= 12 x = 60, suy Ta2a + b ^ 26 Vi a < ; /? < nen 2a + b< 24 Vay trudng hpp khong xay ra, Trudng hap Miu l a a ; ; ; & ; a + (sap xe'p theo thii tu tang din) Khi dd tong cac sd lieu la 2a + + 34 - 12 x = 60 Suy 2a + & = 26 hay ^ - - a = ( - a ) Vay b chan, tiie la b cd dang b = 2c Suy c - 13 - a Vi < a + 18 va a = - c n e n 2c < - c + = - c Vay 3c < 31 hay c < lO.Via < n e n c > - = Khi dd ft > 10 > Tdm lai < c < 10 Nhu vay ta cd miu thoa man dieu kien da neu la { - c ; ; ; c ; 31 - c } dd c G { ; ; ; ; ; 10} Cu thd la cae m i u { ; ; ; 10; 26), (5 ; 16; 23}, { ; ; ; 12; | , {4 ; 18; 22}, {6; ; ; 14; 24), (3 ; ; 21} 259 38 3sin(a - P) = ^iniP - a + a) = sina eos(a - p) - sin(a - P)cosa, tif ta cd ^ sin a (3 + cosa)sin(or - p) = sina cosia - p) (*), vay tan(a - P) = ^ iChu y cos(a - p) ^ vi neu cos(« - y^ = thi tir (*) ta suy smia- 39 p) = 0, vo li) Ta cd : cos"x+ 2cosaeosy9cosx= cos/[cos(7c- ia + p)) + c o s a c o s ^ = cos/[-cosa c o s ^ + sinorsin^+ 2cosacos;?] = c o s / c o s ( « - y ^ T = -cos(a + ^ c o s ( a - > ^ = sin'asin ^ - c o s '' acos'p = sin^asin"y5-(l -sin^a)(l -sin'^y^^-l + s i n " a + s i n V = l-cos"a-eos"yft 40 Dat t = t a n ^ , thi 4.^—^^^ + eos a ? — + = 4r^- 2(1 + t^) + = 2r^ + 1, -> a cos' — nen gia tri nho nha't dat dupe la t = 41 a) a ^ ~ + kn \ a ^ — + k— : a ^ — + k— voik &I, Hudng ddn Cd the vie't miu (cosa + cos7a) + (cos3a + cos5a) = 2cos4a(eos3a + cosa) = cos a cos a cos 4a b) Hudng ddn Viet tu thiic 2sin4a(cos3a + cosa) 42 260 Diing cdng thiic bac va cong thdc bien ddi tong tich MUCLUC Trang Chi/ang I MENH DE - TAP HCJP A NHUTNG KIEN T H Q C CAN NHCJ B DE BAI §1 Menh de va menh de chira bien §2 Ap dung menh de vao suy luan toan hpc §3 Tap hop va cac phep toan tren tap hpp 11 §4 Sd gan dung va sai sd 12 Bai tap on tap chUdng I 12 Gidi thieu mpt sd cau hoi tr&c nghiem khach quan 14 C DAP SO - H I J N G D A N LCfl GIAI ChLfOngll HAIVISO 16 26 A NHLfNG KIEN T H Q C CAN NHd 26 B DI BAI 29 §1 Oai cUOng ve ham sd 29 §2 Ham sd bac nhat 32 §3 Ham sd bac hai 34 Bai tap on tap chucfng II 36 Gidi thieu mot sd cau hoi trac nghiem khach quan 37 C O A P S O - HLTCJNG D A N - LC(I GIAI 39 261 Chuong III PHUONG TRINH BAC NHAT VA BAC HAI A NHIJNG KIEN THCTC CAN NHCJ 55 55 B DE BAI 58 §1 Dai cUOng ve phUdng trinh 58 §2 Phuong trinh bac nhat va bac hai mpt an 59 §3 Mpt sd phuong trinh quy ve phuong trinh bac nhat ho§c bac hai 62 §4 Phuong trinh va he phuong trinh bac nhat nhieu an 63 §5 Mpt sd vi du ve he phuong trinh bac hai hai an 66 Bai tap on tap chUdng III 67 Gidi thieu mpt sd cau hoi trac nghiem khach quan 70 C D A P S O - HaCJNG D A N 71 L d i GIAI Chaang IV BAT DANG THlTC VA BAT PHUONG TRINH A N H Q N G K I E N T H Q C CAN 262 NHCJ 99 99 B D E B A I 102 §1 Bat dang thu'c va chirng minh bat dang thCfc 102 §2 Dai cuong ve bat phuong trinh 106 §3 Bat phuong trinh va he bat phUOng trinh bac nhat mpt an 107 §4 Dau cua nhj thu'c bac nhat 109 §5 Bat phuong trinh va he bat phuong trinh bac nhat hai I n 110 §6 Dau ct!ia tam thufc bac hai 111 §7 Bat phuong trinh bac hai 112 §8 Mpt sd phuong trinh va bat phuong trinh quy ve bac hai 114 Bai tap on tap chuong IV 116 Gidi thieu mpt so cau hoi trac nghiem khach quan 120 C DAP SO - HUdNG D A N 122 LCfl GIAI Chuang V THONG KE 1^2 A N H Q N G K I E N T H Q C C A N NHCJ 172 B.OEBAI 173 §1 Mpt vai khai niem md dau 173 §2 Trinh bay mpt mau so lieu 173 §3 Cac sd dSc trUng cua mau sd lieu 175 Bai tap on tap chuong V 180 Gidi thieu mpt sd cau hoi trac nghiem khach quan 181 C D A P S O HLTdNG D A N - LCJI GIAI Chirang VI GOC LUONG GIAC VA CONG THLfC LUONG GIAC 183 193 A N H Q N G K I E N THCTC C A N NHCJ 193 B DEBAI 195 §1 Goc va cung lupng giac 195 §2 Gia trj lupng giac cCia gde (cung) lupng giac 195 §3 Gia tn lupng giac cua cac goc (cung) c6 lien quan dSc biet 200 §4 Mpt sd cong thtfc lupng giac 204 Bai tap on tap chuong VI 206 Gidi thieu mpt sd cau hoi trac nghiem khach quan 208 C D A P S O - HUCJNG D A N - LC!l GIAI 210 Bai tap on tap cuol nam 238 A DE BAI 238 B D A P S O - HLTCJNG D A N L0\ GIAI 243 263 Chiu track nhiem xuat bdn : Chu tich HDQT kiem Tdng Gi^m d6'c N G T R A N AI Pho Tdng Giam d6c kiem Tdng bien lap NGUYfiN QtJ'f THAO Bien tap Idn dau HOANG XUAN VINH - D^NG MINH THU Bien tap tdi bdn : HOANG VIET Bien tap Id thuat Kltv NGUYET V I £ N - TRAN THANH HANG Trinh bay bia BUI QUANG TUAN Sua bdn in HOANG VIET Che bdn C N G TY c PHAN THIET K£ VA PHAT HANH SACH GIAO DUG BAI TAP DAI SO 10 - NANG CAO Ma sd : NB003T1 In 10.000 ban, (OD:04BT/KH11) kh6l7x24cm Tai Nha in Bao Ha Nam Sd29 - O Ld Hoan - TP Phu Ly - Ha Nam S6in:410.S6XB:01-2011/CXB/850-1235/GD In xong va nop lau chieu thang 01 nam 2011 264 i VUONG MIEN KIM CUONG CHAT LUONG QUOC TE HUAN CHUONG HOCHI MINH SACH BAI TAP LCJP 10 BAI TAP DAI SO 10 BAI TAP HlNH HOC 10 BAI TAP TIENG ANH 10 BAITAPTI^'NGPHAPIO BAI TAP VAT LI 10 BAITAPHOAHOCIO BAI TAP TIN HOC 10 BAITAPTIENGNGAIO BAI TAP N G Q V A N 10 (tap mpt, tap hai SACH BAI TAP LOP 10 - NANG C A O BAI TAP DAI SO 10 BAI TAP HOA HOC 10 BAI TAP HiNH HOC 10 , BAI TAP NGCTVAN 10 (tap mpt, tap hai) • BAI TAP VAT LI 10 , BAI TAP TIENG ANH 10 Ban doc co the mua sach t a i : • Cac Cong t> Sach - Thiet hi truang hoc o cac dia phucmg, • Cong X\ Q? Dau nr \ a Phat tricn Giao due Ha Noi, ]8~B Giang \'o TP, Ha \ p i • Cong l> CP Dau tu \a Phat tricn Giao due Phtroiig Xam 23 I \gLi\cn \"an Cii Quan TP HCM • Cong t_\ CP Dau tir \ a Phat tricn Giao diic Da Nang 15 Ngu\cn Chi Thanh TP, Da N5ng hoac cac cua hang sach cua Nha xuat ban Giao due V i e t N a m ; - T a i T P , Ha NOI : IS" Giang \ o : 232 Ta\ Son : 23 Tranc Tien : 2.^ HanThu>cn : 32E Kim Ma 14 Ngii\cn Khanh Toan : 6'^B Cira Bac - Tai TP Da N:ing : "S PaMeur; 24" Hai Phong - T a i TP 116 Chi Mmli 1(14 Nhii Tin Luu : 2.A Dinh Ticn Hoang Quan : 240 Tran Binh Trong ; 231 Nguyen \"an Cii Quan - Tai TP t an Tho : 5 Duoiii: ^(l - Tai Website ban >aeh true iu\cn : \\\\\\.saeh24.\n Website: \ \ \ \ " n \ b " d v n Gia:14.600d 9349Q4 " 023948