Thiết kế bài giảng đại số 10 nâng cao (tập 2) phần 1

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

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 p]»<«*iig t r i n l i

V6 mat hinh thiic, bat phuong trinh dugc trinh bay co ban nhu' phuong trinh, nhung chi khac d day da xay dung quan he thii tu tren tap hgp sd thuc

Ndi dung co ban la trinh bay ve bat phuong trinh mdt an ma d do cung dua ra

cac quy tic co ban de tim nghiem ciia chiing Dac biet la ndi dung ve kinh dien

giai bat phuong trinh bae nhat va bat phuong trinh bae hai Trong chuong nay cung dua them khai niem ve bat phuong trinh bae hai hai in, d dd cd dang dap ciia bai loan kinh te bai toan tdi uu

Chiing minh thanh thao cac bat ding thirc, van dung linh hoat cac quy

tic: chuyen ve nhan hoac chia hai \6 cua mdt bat ding thuc vdi mdt sd

Giai mdt each thanh thao cac bat phuong trinh bae nhat xa bat phuong

trinh bae hai

•DBiet xac dinh tap nghiem cua bat phuong trinh bae nhat hai in, tir do manh nha giai cac bai toan kinh te rat don gian

PHAN 2 CAC B A I SOAKT

§1 Bat dang" t h d c va cluitng m i n h b a t

dang^ thu'c (tiet 1, 2, 3)

I M U C T I E U

1 Kien thiic

HS nim dugc :

Cac khai niem ve bat ding thirc

Cac tinh chat ciia bat ding thiic

Cac bat ding thiic co ban va cac tinh chat cua nd

He thdng dugc cac bat ding thuc, tir dd hinh thanh cac phuong phap chiing minh cac bat ding thuc

Van' dung cac bat ding thiic Cd-si, bat ding thiic cd chua dau gia tri tuyet ddi de giai cac bai tap cd lien quan

Biet tim gia tri Idn nhat va nhd nhat ciia mdt ham sd, mot bieu thiic dua vao bat ding thiic

2 KT nang

HS phai chiing minh dugc cac bat ding thiic don gian

Van dung thanh thao cac tinh chat cua bat ding thirc de bien ddi tir dd

giai dugc cac bai toan \'6 chiing minh bat ding thiic, tim gia tri Idn nhat, nhd

nhat cua ham sd, ciia mdt bieu thiic

3 Thai do

Tu giac, tich cue trong hgc tap

Biet phan biet rd cac khai niem co ban, cac tinh chat va van dung trong tirng trudng hgfp cu the

Tu duy cac van di cua toan hgc mdt each logic va he thdng, budc diu

CO tu duy cue tri trong qua trinh sang tao

II CHUAN BI CUA GV VA HS

Can dn lai mot sd kien thiic da hgc d ldp dudi

III PHAN PHOI THCH LUONG

Bai nay chia lam 3 tiet :

Tiet 1 : Tit ddu den het phdn 2

Tiet 2 : Tit phdn 3

Tiet edn Iqi: chda bdi tap

IV TIEN TRINH DAY HOC

Nhirng ket luan sau day, ket luan nao dung?

(a) x~ + X + 1 > 0 vdi mgi x G M

B BAI Mdi

HOAT DONG 1

1 On Tap va bo sung tinh chat ciia bat ding thijfc

• GV neu van de:

HI Hay neu khai niem ve bat ding thiic _

H2 The nao la chiing minh bat ding thuc?

H3 a +h < - 2 cd phai la bat dang thiic hay khdng? neu phai thi day la bat dang

thiic diing hay sai?

• GV neu dinh nghia:

Cdc menh de dang a < b hoac "a > b" "a > b" "a < b"

dugc ggi la nhiing bdt ddng thdc

Hoat dong ciia HS

Ggi y tra 161 cau hoi 1

a < b < = > a - b < 0

a - b < 0 < ^ a < b

Ggi y tra idi cau hoi 2

a - b - l < O c : > a < b + 1

Tinh chat ciia bat ding thiic

GV: Cho HS dgc vd xem xet trang 104 SGK Sau do chia HS thanh 4 nhom, mdi nhom thao luan vd cii dai dien len bdng thuc hien thao tdc dien vao chS trdng

Nhom 1 Dien ddu > hoac < vao cho tiring

Tinh chdt Dieu kien

a <b a + c <b + c

Ten goi

Cdng hai ve cua bat ding thirc vdi mdt so

a + c > b < : ^ a > b - c ;

a > b > 0 va U G N * ^ a " > b " ;

a > b > 0 = 5 > ^ / a > ^ y ^ ; a>h => yfa > ifb

• GV neu vi du 1 trong SGK va cho HS lam, ggi y bing cac cau hdi sau:

HI Binh phuong hai ve cua mdt bat ding thirc, ta dugc bat ding thiic ciing chi6u Diing hay sai?

H2 Neu sai can bd sung dieu kien gi de dugc khing dinh diing?

H3 Gia sit v2 + V3 > 3 hay binh phuong hai ve va so sanh

• GV neu quy udc trong SGK

• Neu vi du 2 trong SGK va cho HS lam, ggi y bing cac cau hdi sau:

HI Hay chuyen ve va dua bat ding thiic ve dang : f(x) > 0

H2 Hay chiing minh f(x) > 0 la bat ding thirc diing

• Neu vi du 3 trong SGK va cho HS lam, ggi y bing cac cau hdi sau:

HI Hay neu mdi quan he giira cac canh trong tam giac

2 2 2

H2 Giai thich vi sao a > a - (b - c)

H3 Giai thich vi sao (a - b + c)(a + b - c) = a^ -(b-c)^

H4 Hay lam tuong tu va chiing minh bat ding thiic da cho

2 Bat dang thurc ve gia tri tuyet ddi

• GV neu cac bat ding thiic trong SGK

-\a\<a< \a\ vdi mgi a G R

|x| < a <=> - a < X < a vdi a > 0

\x\>a <^ x <-a hoac v > a vaia >0

• GV neu bat ding thirc quan trgng sau:

\a\ - \b\ <\a + b\< \a\ + \b\ (vdi mgi a, b e R)

GV cho HS chiing minh bat dang thiic tren (ke ca |H1| bing HD sau)

10

Hoat d o n g cua G V Hoat dong cua H S

b i n g each sir dung cau hdi 1

Ggi y tra 161 cau hoi 1

Ggi y tra 161 cau hdi 3

Ta cd |a| = |a + Z) - Z?| < |a + Z?| + \-b\

= \a + b\ + \b\

Chuyen ve ta dugc DPCM

HOAT DONG 2

2 Bat d^ng thiifc trung binh cong va trung binh nhan

a) Do! vdi hai so khong am

• GV neu dinh li

Vdi mgi a > 0, b > 0 ta cd

a + b i—r

> yjab

2

Sau dd GV neu cac cau hdi

HI Hay phat bieu dinh li bing Idi

De chung minh dinh li, GV neu cac cau hdi sau:

H2 Dien cac dau > < > < vao chd trdng sau:

^ ' ^ = - - ( a + b- 2 ^ ) = - - ( ^ - V^)2 0,

2 2 2

H3 Hay ket luan va chi ra trudng hgp dau bing xay ra

H4 Van dung dinh li hay chii'ng minh I tan x + cot x 1> 2

Thuc hien H 2

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

riit ra bat dang thiic

Hoat dong cua HS Ggi y tra 161 cau hdi 1

• GV neu vi du 4 va hudng din HS lam theo cac cau hdi sau:

HI Hay phan tich \'e trai thanh tong ciia nhCing sd cd dang nghich dao ciia nhau H2 Hay ap dung bat ding thuc Cd-si

12

• GV phat bieu he qua bing Idi:

HE QUA

NcAt hai sd duang thay doi nhung co tong khong ddi thi tich ciia chiing lini nhdt khi hai sd do bdng nhan Nen hai sd duang thay doi nhung cd ticli khong ddi thi tong ciia chiing nho nhdt khi hai so do bang nhau

Sau dd hudng dan HS chiing minh theo cac cau hdi sau day:

H4 x+ y nhd nhat khi nao?

H5 Ap dung he qua hay tim gia tri nhd nhat cua bi6u thiic ciia bieu thirc :

• GV neu iing dung :

Trong tdt cd cdc hinh chif nhdt cd cimg chii vi, hinh viiong cd dien tich lan nhdt Trong td'i cd cdc hinh chit nhdt cd ciing dien tich, hinh viidng cd chu vi nho nhdt

• GV neu vi du 5 va hudng din HS thuc hien theo cac cau hdi sau:

HI Chiing minh ring f(x) > 2V3

H2 Dau bing xay ra khi nao?

b) Ddi vdi ba sd khdng am

• GV neu dinh li

a + b + c

^Jabc <» a = b- c

(vdi mgi a, b, c > 0)

Sau dd GV dua ra cac cau hdi sau:

HI Hay phat bieu dinh li bing Idi

H2 Neu bd di dieu kien ba sd khdng am thi dinh li edn diing hay khdng? hay neu mdt vi du

• GV neu vi du 6

Sau dd hudng din HS chiing minh bing cac cau hdi sau day:

HI Hay ap dung dinh li ve bat ding thiic Cd-si cho ba sd a, b, c

H2 Hay ap dung dinh li v6 bat dang thiic Cd-si cho ba sd

H3 Hay chiing minh bat ding thiic tren

H4 Dau bing xay ra khi nao?

Phat bieu ke't qua tirang tir he

qua tren cho trudng hgp ba sd

duang

Cau hoi 2

Ne'u bd di dieu kien ba so

duang thi ke't qua con dung

nhat khi ba sd do bing nhau Neu ba

sd duong thay ddi nhung cd tich khdng ddi thi tong ciia chiing nhd nhat khi ba sd dd bing nhau

Ggi y tra 161 cau hdi 2

Khdng

14

T O M T A T B A I H O C

1 Cac bat dang thirc cd dang a < b, a > b, a < b, a > b

2 Cac tinh chat ciia bat ding thiic

a <b ci> \fa <y[b

3 Bat ding thiic Cd-si:

Trung binh nhan ciia hai sd khong dm nho han hoac bang trung binh cong ciia chiing

^ t j ^ Va,b>0

ab <

a + b Dang thicc yjab = xay ra khi vd chi khi a = b

Cac he qua:

He qua 1

Ne'u X, y cimg duang vd cd tong khdng ddi thi tich xy Idn

3 Hay chgn khing dinh diing trong cac khing dinh sau :

(a) X + Ixl > 0 (b) X - Ixl > 0

(c)-2x+ x <0

16

(d)x + 2 X < 0

Tra lai (a)

4 Hay dien cac dau (>, <, =) vao cac chd trdng thich hgp sau

(a) V2 V3; (b) Vs VV

(c) 72 + Vs 73 + V? ; (d) 7I0 722

Tra lai

Cau Di6n

Cau Dien

10 Hay chgn ket qua diing trong cac ket qua sau

(a) a -H 1 > a -K a Va e :i: (b) a"^ + 1 < a'' -h a Va G J<;

18

b 2 (d) a < l

14 Chgn bat ding thiic dung trong cac bat ding thiic sau

18 Chgn ket qua diing trong cac ket qua sau

(a) a+ b + c > 3¥abc ; ( b ) - a - b - c < - 3¥abc ;

(c) - 7 a - 7 6 - 7 c < - 3 ^ / 7 a + 7 ^ + 7 c ; (d) 7 o - 7 ^ + 7 c > 3 x / 7 a + 7 ^ + 7 c

Trd Idi (c)

20

Ggi y tra Idi cau hdi 1

Hai so a va b ciing dau

Ggi y tra Idi cau hdi 2

GV: Hudng ddn hgc sinh Idm bdi tap nay a nhd

- On lai tinh chdt ba canh ciia tam gidc

- Cdc tinh chdt ciia bdt ddng thiic

C a u hdi

C a u hdi 1

Ne'u ba canh ciia tam giac la a

b, c Tinh nira chu vi p ciia tam

giac

C a u hdi 2

Hay tinh p - a, p - b, p - c

Ggi y tra 161 Ggi y tra Idi cau hdi 1

p - b = 2

b + a - c

p - c = 2

Cau hdi 3

Chimg minh bai toan tren

Goi y tra Idi cau hdi 3

Vi — > 0 va b < a

ab

Bai 3

GV: Hudng ddn

HS dn tap lai cdc tinh chdt ciia bdt ddng thicc

- Mot sd ki ndng bie'n ddi bdt ddng thii'c

Cau hdi Cau hdi 1

Hay dua bat ding thire ve dang

Ggi y tra Idi cau hdi 2

Nhan ca hai ve vdi 2 ta cd

2a^ + 2b2 + 2e^ -lab - 2bc - 2ca > 0

«> (a - b)2 + (b - c)2 + (c - a)2 > 0

Ggi y tra Idi cau hdi 3

a - b = b - c = c - a = 0 tire la

a = b = c

Bai 4

Hudng din cau b)

Cau hdi Cau hdi 1

Nhan xet ve dau cua hai ve

ciia bat ding thiic

Ggi y tra 161 Ggi y tra 161 cau hdi 1

Hai ve ciia bat ding thiic khdng am

Ggi y tra Idi cau hdi 2

22

Cau hdi 2

Hay binh phuong hai ve va

chung minh bat ding thiie

(7a + 2 + 7a + 4) < (73" + 7a + 6 ) '

hay la + 2 + a + 4 + 27(a + 2)(a + 4)

< a + a + 6 + 27a(a + 6)

nen ^(a + 2)(a + 4) < 7a(a + 6)

Do dd (a + 2)(a + 4) < a(a + 6) hay la a^ + 6a + 8 < a^ + 6a nen 8 < 0

Dd la dieu vd li

Vay 7a + 2 + 7a + 4 > 7a + 7a + 6 (a > 0) Cau a) la dang dac biet cua cau b) vdi a = 2002

Bai 5

Hudng ddn hgc sinh Idm bdi tap nay

- On lai dinh li bdt ddng thiic Cd-si cho hai so khdng dm

Cau hdi Cau hdi 1

Nhan xet ve dau ciia hai so

Hai so nay cd dau duang

Ggi y tra Idi cau hdi 2

Bai 6

Hudng ddn hoc sinh idm bdi tap nay a nhd De Idm bdi tap nay HS can dgc kl lai khdi niem vd tinh chdt ciia bdt ddng thitc, cdc hang ddng thiic ddng nhd

24

Cau hdi Cau |idi 1

Hay so sanh a+b va

Hay cdng ve vdi ve cac bat

ding thiic tren va riit ra ket

luan

Ggi y t r a Idi Ggi y tra 161 cau hdi 1

Ta cd a - b va c la hai so khdng am, han nira a - b < c, binh phuang hai ve cua bat ding thii'c nay ta cd

a^ +b^ < c^ +2ab

Ggi y t r a Idi cau hdi 2

b^ +c^ <a^ +2bc a^ +c^ <h^ +2ac

Ggi y tra Idi cau hdi 3

GV tu rut ra ke't luan

Bai 9

Hudng ddn hgc sinh Idm bdi tap ndy a nhd De Idm bdi tap ndy, HS can dgc kl lai khdi niem vd tinh chdt ciia bdt ddng thitc, cdc hdng ddng thitc ddng nhd, cdch phdn tich thdnh nhdn tit

Cau hdi Cau hdi 1

Hay xet dau cua hai sd x + 3

va 5 - X

Cau hdi 2

Tong hai sd bing bao nhieu?

Ggi y tra Idi

Ggi y tra Idi cau hdi 1

Hai sd nay khdng am

Ggi y tra 161 cau hdi 2

Tong hai sd bing 8 khdng ddi

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Cau hdi 3

Hay ap dung he qua ciia bat

ding thiic Cd-si va ket luan

Ggi y tra Idi cau hdi 3

Gia tri nhd nhat la f(-3) = 0

Bai 13

Hudng ddn hgc sinh lam bdi tap ndy De Idm bdi tap ndy, HS edn dgc ki lai khdi niem vd tinh chdt ciia bdt ddng thitc, bdt ddng thitc Cd-si vd he qua cho hai sd khdng dm

Hay bie'n ddi / (x) = x - 1 H 1-1

x - 1

Ap dung bdt ddng thitc Cd-si cho hai sd'x - 1 vd

Gia tri nhd nha't la 1 + 2 7 2

x - 1

Luyen tap (tiet 4)

I MUC TIEU

1 Kien thirc

HS dn tap lai dugc :

Cac khai niem ve bat ding thirc

Cac tinh chat cua bat ding thiic

Cac bat ding thiic co ban va cac tinh chat ciia nd

He thdng dugc cac bat ding thitc, tir dd hinh thanh cac phuong phap chiing minh cac bat ding thiic

Van dung cac bat ding thiic Cd-si, bat ding thiic cd chiia dau gia tri tuyet ddi de giai cac bai tap cd lien quan

Biet tim gia tri Idn nhat va nhd nhat cua mdt ham sd, mot bieu thiic dua vao bat ding thiic

2 KT nang

HS phai chiing minh dugc cac bat ding thirc don gian

Van dung thanh thao cac tinh chat ciia bat ding thii'c de bien ddi, tir do giai dugc cac bai toan ve chiing minh bat ding thiic, tim gia tri Idn nhat, nho nhat cua ham sd, cua mot bieu thirc

Giai dugc cac bai tap trong SGK

Thdng qua cac bai tap luyen tap de hoan thien he thdng kien thiic ve bat ding thirc

Thdng qua cac bai tap luyen tap se cd nhieu phuang phap chiing minh

mdi v6 bat ding thiic

3 Thai do

Tu giac, tich cue trong hgc tap

Bie't phan biet rd ca dang chiing minh bat ding thiic

Tu duy cac van de ciia toan hgc mdt each Idgic va he thdng, budc diu

cd tu duy cue tri trong qua trinh sang tao

28

II CHUAN BI CUA GV VA HS

1 Chuan bi ciia GV

GV chuan bi chira mdt so bai tap tai ldp, mdt sd bai edn lai hudng din

HS lam tai nha

Chuan bi phan mau va mdt sd cdng cu khac

2 Chuan hi ciia HS

Can dn lai mdt sd kien thirc da hgc d bai 1

HI PHAN PHOI T H d l LUONG

Bai nay chia lam 1 tiet :

IV TIEN TRINH DAY HOC

Nhirng ke't luan sau day, ke't luan nao dung?

(a) x^ + X + 1 > 0 vdi mgi x e M

B BAI M 6 |

HOAT DONG 1

Bai 14

- HS can dn lai bat ding thiic Cd-si cho ba so khdng am

- Ap dung true tiep dinh li nay d6 chLhig.minh bai toan

GV hudng din HS lam bai nay tai ldp theo hudng din sau:

Ggi a, b la cac canh tay ddn ben phai \'a ben trai cua can dia

Cau hdi Cau hdi 1

Trong lan can dau sd cam

dugc can la bao nhieu?

Cau hdi 2

Trong lan can sau khdi

lugng cam la bao nhieu?

Cau hdi 3

Trong hai lan can khdi lugng

cam la bao nhieu?

Cau hdi 4

Hay ket luan

Goi V tra Idi

Ggi y tra Idi cau hdi 4

Khach hang mua nhieu hon 2 kg

30

^ 1.2 2.3 3.4 n(n + l)

b) Hudng din HS lam tai ldp

Cau hdi Cau hdi 1

Chirng minh bai toan

Ggi y tra Idi

Ggi y tra Idi cau hdi 1

Ggi y tra Idi cau hdi 3

GV cho HS ket luan bai toan

HOAT DONG 4

Bai 17

De lam bai tap nay HS can dn tap va van dung cac kien thuc sau:

- Dinh li va he qua ciia bat ding thiic Cd-si

- Cac tinh chat ciia bat ding thirc

Hudng din HS lam tai ldp

Cau hdi Cau hdi 1

Hay tinh A'

Cau hdi 2

Ap dung bat ding thiic Cd-si

cho bieu thiic

2 7 ( x - l ) ( 4 - x )

Cau boi 3

Giai bai toan

Ggi y tra Idi Ggi y tra Idi cau hdi 1

De lam bai tap nay HS can dn tap va van dung cac kien thirc sau:

- Hing ding thiic dang nhd

- Cac tinh chat cua bat ding thiic

Hudng din HS lam ve nha

(a + b + c)- < 3(a^ + b" + c" c^ a^ + b^ + c^ + 2ab + 2bc + 2ca < 3(a^ + b^ + c^)

« 2ab + 2bc + 2ca < 2(a^ + b" + c^)e> (a - b)^ + (b - c)^ + (c - af > 0

HOAT DONG 6

Bai 19

De lam bai tap nay HS cin dn tap va van dung cac kien thiic sau:

32

- Dinh li va he qua cua bat ding thirc Cd-si

- Cac tinh chat cua bat ding thuc

Hudng din HS lam tai ldp

Cau hdi Goi V tra Idi Cau hdi I

Ap dung bat ding thiic Cd-si

cho hai cap so a va b ; c va d

Ggi y tra Idi cau hdi 2

TCr tren suy ra

Ggi y tra Idi cau hdi 3

De lam bai tap nay HS can dn tap va van dung cac kie'n thiic sau:

- Hing ding thiic dang nhd

- Cac tinh chat ciia bat ding thiic

- Bat ding thiic Cd-si

Hudng din HS lam ve nha

a) (X + y)^ = x^ + y^ + 2xy < 2x^ + 2y^ = 2 ^ | x + y | < 72

b) 15^ = (4x - 3y)^ < (x^ + y^)(4^ + (-3)^) = 25(x^ + y^) => x^ + y^ > 9

Cd the chiing minh bing nhieu each khac

BO SUNG KIEN THUC

Bdt ddng thiic Cd-si tong quat:

Cho n sd khdng am : aj 03, , a„, khi dd : -^ ^—LJ n > iila^an-.-a

n

Dau bing xay ra khi: a^ = a2 = = a„

2 Bait dang thiirc Bunhiacdpxki:

Cho bd'n sd a, b, c, d Khi dd (ac + bd)'^ <(a'^ +b^)(c'^ +d'^)

Dau bing khi — = —

c d

Bat ding thiic tdng quat cd ten: Cdsi- Svac

Chohaibdnsd ai,a2, ,a,, va b^,b2, ,b,^ Khi dd

Dau bing khi: J - = ^ a,

34

Neu dugc dieu kien xac dinh cua bat phuong trinh

Sau khi hgc xong bai nay HS giai dugc cac bat phuang trinh don gian Bie't each tim nghiem va lien he giiia nghiem cua phuang trmh va nghiem cua bat phuong trinh

Xac dinh mdt each nhanh chdng tap nghiem cua cac bat phuang trinh va

he bat phuong trinh don gian dua vao bien ddi va lay nghiem tren true sd

3 Thai do

Bie't van dung kie'n thiic ve bat phuang trinh trong suy luan logic

Dien dat cac van de toan hgc mach lac", phat trien tu duy va sang tao

II CHUAN BI CUA GV VA HS

1 Chuan hi ciia GV:

De dat cau hdi cho HS, trong qua trinh day hgc GV can chuin bi mot sd kie'n thiic ma HS da hgc d ldp dudi, ching han :

- Cac bat phuang trinh bae nhat da hgc

- Cach lay nghiem ciia he bat phuang trinh tren true sd

Chuin bi phan mau va mdt sd cong cu khac

2 Chuan hi ciia HS :

Cin dn lai mot so kien thiic da hgc d ldp dudi

HI PHAN PHOI THCII LUONG

Bai nay day trong 1 tiet

IV TIEN TRINH DAY HOC

Hay xac dinh tinh diing - sai ciia cac menh de sau day:

1) Ne'u hai phuong trinh f(x) = 0 vag(x) = 0 vd nghiem thi hai bat phuang trinh f(x) > 0 va g(x) > 0 cung v6 nghiem

2) Neu ham y = f(x) cd dd thi nim hoan toan phia tren true hoanh thi bat

phuang trinh f(x) < 0 v6 nghiem

B BAI M 6 |

HOAT DONG 1

1 Khai niem bat phiTdng trinh mot an

• GV neu dinh nghia

36

Cho hai ham sd y - f(x) vd y = g(x) cd tap xdc dinh Idn lugt Id U^^

vd IT^, Ddt 'J^ = ^J^f n y^^, Menh de chita bie'n cd mot trong cdc dang fix) < g(x), f(x) > g(x), f(x) < g(x), f(x) > g(x) dugc ggi Id

mdt bdt phuang trinh mot dn; x ggi Id dn sd (hay dn) vd U^ ggi Id

tap xdc dinh ciia bdt phuang trinh

So XQ e y^ ggi Id mot nghiem ciia bdt phuang trinh f(x) < g(x)

ne'u menh de /(XQJK g(xQ) Id dimg Khdi niem ndy cimg dugc dinh nghJa tucmg tu cho cdc bdt phuc/ng trinh dang

fix) > g(x),f(x) < g(x) vd fix) > g(x)

Sau dd GV neu cac chii y sau:

- Khai niem nay cung dugc dinh nghia tuong tu cho cac bat phuang trinh dang

Bieu dien tap nghiem cua mdi

bat phuang trinh : - 0,5x > 2

bdi cac ki hieu khoang

hay doan

Cau hdi 2

Bieu dien tap nghiem cua mdi

bat phuong trinh : x| < 1 bdi

Hoat ddng cua H S Ggi y tra Idi cau hdi 1

T = ( - o o ; - 4 )

Ggi y tra Idi cau hdi 2

T = [ - l ; l ]

HOAT DONG 2

2 Bat phLfdng t r i n h tUdng d i / d n g

• GV neu dinh nghia

Hai bdt phuang trinh dugc ggi Id tuang duang ne'u chiing cd ciing

Sai Ching han x = 1 khdng thoa man

Ggi y tra Idi cau hdi 2

Diing

• GV neu chu y trong SGK va neu vi du 1

Sau do dat ra cac cau hdi sau cho HS tra Idi nhim cimg cd kie'n thircmue nay

HI Hai bat phuong trinh von ghiem thi cd tuang duong khdng?

H2 Hai bat phuang trinh tuong duong tren D la gi ?

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