Lng Vn Thin - GSTT Group

MT S T DUY CH O GII PHNG TRNH - H PHNG TRNH

Cn thnh tho: Phng trnh ng cp, h i xng loi 1 - 2, cc hng ng thc ng nh, bt ng thc v b

bt c bn (c tm tt bn di), mt s phng trnh c bn,...

Gii BPT: cch lm tng t nh PT, HPT.

Lun nhm nghim trc khi bt u lm.

1 - t n ph

- Thy biu thc no xut hin nhiu ln, t n xong thy phng trnh gn th ta t n lm n ph.

- C th dng nhiu n ph gii. Khng nht thit phi t t n. Biu thc gn l s ra c li gii.

- Dng cc php ton cng, tr, nhn, chia, ph ngoc, nhm,... th mi nhn ra c n ph. Thng l chia

1. 2 2 2

1 7

1 13

xy x y

x y xy y

2.

2 2

2 2

1 4

( ) 2 7 2

x y xy y

y x y x y

3.

7 2 5

2 1

x y x y

x y x y

2 - Phn tch thnh nhn t

- Nhm nghim, d on nhn t ri i phn tch. VD: nghim x=y th d on nhn t x-y, ....

- Kt hp vi n ph nhn nhanh ra nhn t. Dng Casio Fx 570MS (Phm CALC) nhm. Hoc nghim ca

thng l nghim p nn ta th vi cc s: 1, 2, 0, 1/2, -1, -2 ... Hy nhm nghim tht gii.

1.

2 22

2 1 2 2

xy x y x y

x y y x x y

2.

2 2 3

2 2 2

5 4 3 2( ) 0

( ) 2 ( )

x y xy y x y

xy x y x y

3.

2 2

2

21

xyx y

x y

x y x y

3 - Dng hng ng thc

- Thy xut hin hng ng thc th nhm li. C ngoc th ph ra. Nhm nghim bit cch tch v nhm thnh hng

ng thc. Thng l 2 3( ) , ( ) ,...a b a b

1.

2 3 2

4 2

5

4

5(1 2 )

4

x y x y xy xy

x y xy x

2.

4 2 2

2 2

2 4 5 0

2 3 15 0

x x y y

x y x y

2.

2 2

3 3

2 1

2 2

y x

x y y x

4 - ng bin, nghch bin

- C 2 hng: f(u)=f(v) m f n iu th u=v hoc f = 0 m gii hn c nghim ca f', f'' ... nhm c full nghim

ca f = 0 th suy ra c l mi nghim ca PT.

- Yu cu k nng tnh on o hm v nh gi bt ng thc tt. Bit cch phn on hm f qua n ph, hng ng

thc, hoc kinh nghim. i khi phi bit chia trng hp nh gi bt.

1.

2

2

20131

20131

x

y

ye

y

xe

x

2.

2

2 2

(4 1) ( 3) 5 2 0

4 2 3 4 7

x x y y

x y x

3. 32 (1 4 ) 2 1 0x x x x

5 - Dng bt ng thc gii pt - hpt

- Dng bt co-si, bunhiacosky, bt hnh hc, cc b bt quen thuc gii.

- Thng p dng cho hu ht cc bi s bin nhiu hn s PT. Bi ton c nghim duy nht.

- Mo: Dng my tnh th nh gi cc v, so snh chng ri chng minh kq mnh d on.

1. 2 2 21 1 2x x x x x x 2.

2

4 2 2

1log log 16 4

log 2

4 8 16 4

xy

y

x

x x xy x x y

3. 2 4 32

8

x y

xy

Lng Vn Thin - GSTT Group

6 - Phng php ng cp

- Lm quen vi cc biu thc ng cp - Nu cha quen, dng n ph pht hin ra nhanh pt ng cp.

- Thng s gp pt ng cp bc 2 nhiu hn, nhng cng lu thm ng cp bc 3,4 cao hn.

- Vi HPT th ch cn m bc - nhn cho l OK.

1. 3 22 1 2 3x x x 2.

3 3

2 2

4 16

1 5(1 )

x y y x

y x

3.

2 4 2 4 2

2

2 2 1 2(3 2 )

3

x y xy y x y

x y x

7 - Lng gic ha

- Nu thy bin b gii hn [-1;1], [-a;a] - hoc biu thc lin quan n cc cng thc lng gic th thng s t bin

x=cos t, sin t, a.cos t,... nu bin t do, khng gii hn th t tan t, cot t,....

- bit chc BT c dng lng gic gii hay ko? ta dng mo nhm nghim (kh din t) :)

1. 3 3 1 0x x 2. 3.

8 - Lin hp

- Nhm nghim (thng chn) ri tc nhm lin hp cho ra nhn t chung x-a vi a l nghim nhm c.

- Mt BT c th c lin hp nhiu ln cho ra nhiu nghim, hoc lin hp 1 pht ra 2 nghim.

1. 23 1 1x x x x 2. 10 1 3 5 9 4 2 2x x x x

9 - Loi trc tip

- Nhm v d on a l nghim duy nht PT. Dng bt ng thc ch ra x>a v x