7/25/2019 TTPT&BPT

1/2

7/25/2019 TTPT&BPT

2/2

2 2

a

a b= cos,

2 2

b

a b= sin

phng trnh a vdng: sin(x ) =2 2

c

a b.

iu kin c nghim: a2

b2

c2

IV. Phng trnhng cpi vi sinx & cosx:aosin

nxa1sin

n1xcosx ...an1sinxcos

n1x ancos

nx=0

Cch gii: Xt cosx = 0 v cosx 0; nu cosx 0, chia2 v ph.trnh cho cosnx a v ph.trnh theo tanx

(hoc xt sinx = 0 v sinx 0; nu sinx 0, chia 2 vph.trnh cho sin

nx a vphng trnh theo cotx).

V. Phng trnhi xngi vi sinx & cosx:

a(sinx cosx) bsinxcosx = cCch gii:

t t = sinx cosx (t2 ) th t2= 1 2sinxcosxVI. Phng trnh dn vh: Dng sinax sinbx = 2, ..., sinax.cosbx = 1, ...:Cch gii:

sinax sinbx = 2 sin ax 1sin bx 1 sinax cosbx = 2 sin ax 1cos bx 1 , ...sinax.cosbx = 1 sin(a b)x sin(a b)x = 2.

Dng cosmx sinnx = 1 (m, n > 2):Cch gii:

cosmx sinnx = 1cosmx sinnx = cos2x sin2xcos2x(1 cosm 2x) sin2x(1 sinn 2x) = 0

2 m 2

2 n 2cos x(1 cos x) 0

sin x(1 sin x) 0

Mt scch gii c bit: xem phn trn.

Phng trnh, bt phng trnh m& logarit

I. Phng trnh m& logarit: Phng php a vly tha, logarit cng cs:

af(x)

= ag(x)

f(x) = g(x) (0 < a 1).[u(x)]

f(x)= [u(x)]g(x)

u(x) 0, u(x) 1f (x) g(x)

u(x) = 1

u(x) 0f (x) 0,g(x) 0

ogaf(x) = ogag(x) f (x) 0f (x) g(x) .

Phng php logarit, mha:

af(x)= bg(x)f(x)ogca = g(x)ogcb (0 < c 1).

ogaf(x) = g(x) f(x) = ag(x).

og(x)f(x) = a a(x) 0, (x) 1f (x) [ (x)]

.

Phng php t n ph:

Phng trnh .a2x.ax= 0: t t = ax> 0.Phng trnh .ax.a x= 0: t t = ax> 0.Phng trnh .a2x.(ab)x.b2x= 0: Chia 2 v

cho b2x

(hoc a2x), t t = (a/b)x> 0. Mt scch gii c bit (xem phn trn).

II. Bt phng trnh m& logarit:

af(x)> ag(x) 0 a 1f (x) g(x) a 1f (x) g(x)

a 0(a 1)[f (x) g(x)] 0 .af(x)ag(x) 0 a 1f (x) g(x) a 1f (x) g(x) a = 1

a 0, a 1(a 1)[f (x) g(x)] 0 a = 1.ogaf(x) > ogag(x)

0 a 10 f (x) g(x) a 1f (x) g(x) 0 .

a 0f (x) 0,g(x) 0(a 1)[f (x) g(x)] 0

.

ogaf(x) ogag(x)

0 a 10 f (x) g(x) a 1f (x) g(x) 0 .

a 0, a 1f (x) 0, g(x) 0(a 1)[f (x) g(x)] 0

.

Ch :

1.0 a b 11 a b

:x x

x xx 0 a b

x 0 a b

.

2. ogaA2= 2oga|A|.3. oga(A.B) =

a aa a

og A og B khi A 0 v B 0og ( A) og ( B) khi A 0 v B 0

.

VMnh HngTrng THPTNguyn Hu Hun

Tm tt

Phng Php Gii

phng trnh& bt phng

trnh

03/2010