Kĩ năng giải phương trình và bất phương trình vô tỉ
Bạn đang xem bản rút gọn của tài liệu. Xem và tải ngay bản đầy đủ của tài liệu tại đây (196.59 KB, 14 trang )
!"
#$#%&
!
"#"$%&'(')*+,-.(.*/0
123'.)24,567/689
%)2')*+,-.(.*/0*
:'",.7;)<"=!>?,"@>?A
B;3()'=)*'CCD
3E )%2)6F44,"$
!4,&EFG3,5H"DH
)67
IJK(,5
C3L)M
4,NO7P$.56*E'E
.')&561*%'CQ.)27A
9%")%"R'2ES')*+,-
.(.*/0"FL!2G'T=/H%+2DHU0)%
"R!,V'/57W/'&6%/6<&
'85RH%2.')*P
;1)R/8.)&,";)<X/6<
!HU02')*'C)Y";
-7
J(8+/4,"=M
>')*'CM?.)2',
Y7
>W3)2')*'C"=
!>?,"@7
'()&
A<'!P'"3.64,56'
"3!4,F7'(P56'<:!4TH%+
RD/";)<H%+/3)3!'<*
5%7
W/! 2G'TT+H,!Q
3D<)%'&.Z/6%3'
[)7=/"D<Q'< !"#"FL!
2D./6'/6U7O'&6\/.6!
'85"](!!'8+/3D
<)%'&.E/6%')&)%.)&'2
3)&'(=/H,/7
'*+&
^2')*'C!C"$!
7/68P$.566*E
!H"$%&=/.H,/7IJK(
,C",,),.)2M
$%$% <=
'
$% >
5)&
1C8/T)&Y),.67/689%
!&*",.':7\/
!Q('_H;2T)",'=')*
'C",!"=/::P2,'&EH
)%27;)<"=!>?,"@ B;
')*'CQ=/.H,/+HCYH/
HR),.87O'&6'<: DHU01/*
82!&*5%
Y"+/5/9%<,67W3"=/*\/,!\/
2!&#'852/Z!
,5PG2'E/68,5" //
YD"$3)2,/67
,-&
."/01234/5467829:7;012390123&
A3./4,6`.E*4,16[,'a
)%"R"4,)*Y",
')*),"5/'=')*"#)%27
bc
Mbdbd ''( =
<=>&J2M
e_ +=+ ''
(.f2M)*)+!,! #/ 0*1 !
2.#3&45,
e
≥+
'
e
−≥⇔ '
67 0
,! 8 6
−==⇔
−==
−≥
⇔
=+
−≥
⇔
+=+
≥+
⇔
g
h
g
h
e
hg
e
bed_
e
_
_
*''
''
'
''
'
''
'
9':;<
=
≥
⇔=
bdbd
bd
bdbd
_
''(
'
''(
dH5";"HM
bd ≥'(
b
<=/>3?5@> ABC;
_ += '
<=>?&J2M
''' _h −=−−+
7
(.f2MKM
_
h ≤≤− '
dib7
'''''''' −+−−+−=+⇔−+−=+⇔ bbd_d__h_h
j_
_
bbd_db_d
_
bbd_d_
_
_
=⇔
=+
−≥
⇔
−−=+
≥+
⇔−−=+⇔ '
''
'
'''
'
'''
7
%/"Hdib,*6SkL,#7O&6<4,"#Sk
Nhn xt: =3?
'−
05D."
6C EF2+.+G/0F+!H
?, 8 7
_bc
Mbdbd ''( <
<
≥
>
⇔<
bdbd
bd
bd
bdbd
_
''(
'(
'
''(
<=>@&J2M
_l_
_
+<+− '''
db
J2M
−<+−
≥+−
>−
⇔
__
_
b_dl_
l_
_
bd
'''
''
'
<−−
+
≥
−
≤
>
⇔
e_
_
je
_
je
_
_
''
*''
'
<<−
+
≥
−
≤
>
⇔
e
_
je
_
je
_
'
*''
'
e
_
je
<≤
+
⇔ '
7
ebc
Mbdbd ''( >
≥
≥
<
≥
⇔>
bdbd
bd
bd
bd
bdbd
_
''(
'
'
'(
''(
<=>A&J2)M
e
j
e
e
bld_
_
−
−
>−+
−
−
'
'
'
'
'
IJK7%LMNNOP
J2MKM
h≥'
)
−>−
≥−
<−
≥−
⇔−>−⇔−>−+−⇔
__
_
__
b_dbld_
_
_
l
_bld_jebld_
''
'
'
'
'''''
eh
meh
m
−>⇔
≤<−
>
⇔ '
'
'
<=>B&J2M
l_
_
+=++ '''
J2M
+=+
−≥
⇔
+=+
−≥
⇔
+=++
≥+
⇔
_______
bdl
l
bdl_
''
'
''
'
'''
'
==⇔
=−
−≥
⇔ _
h
_h
''
''
'
<=>C&J2M
7_b_dbd
_
''''' =++−
(.f2MKM
dib
_
=
≥
−≤
'
'
'
7
b_db_d_hb_bdd__
_____
−=−+⇔=+−++⇔ '''''''''''
____
b_db_dh −=−+⇔ '''''
d."Hdibb
( )
=
=
⇔=−⇔
n
g
gn
_
'
'
''
dL,dibb7
Qua v d trên, lưu cho hc sinh cc đim sau:
QP$/>3R>5;
<'SN+.2.F6
<
_____
_
−=−+⇔=++−⇔⇒≥ '''''''
n
g
hhnhh
__
=⇔+−=−+⇔ '''''
IP
<
bbdd_b_dbd_ ''''''' −−=−−−+−−⇔⇒−≤
n
g
_____
_
=⇔+−=−+⇔−=−−+−⇔ '''''''
I+/GP
*2.F T/+;'SN'S
n
g
MP70 U3#VW.X+4.,/@
o7 =
JY& V,
≥
690
≤
77 −−=
<=>D&J2M
eee
e__ −=−+− '''
7
(.f2M
e_b_db_bddee_
ee
e
−=−+−−−+−⇔ ''''''
dib
be_bd_bdd
e__
e
eee
=−−−
−=−+−
⇔
'''
'''
7
_
e
p_p ===⇔ '''
Qua v d trên, lưu cho hc sinh cc đim sau:
P753VW0 U;
qobe_bd_bdde_b_db_bddee_
e
ee
e
=−−−⇔−=−+−−−+− '''''''''
61: 0
U,!5+:0 U Z*[ -V T\
42.6]/ ? 8:0 U
5 236^YG':;
7bde_
e
_
ee
e
_
ee
=⇔=−⇔−=++−−+⇔−=++− '''''''
)'SN/ 4'SN,!_.T6
P*"GU>;
eee
=±
+0`C@ Y
bdebd
eee
±±±=±
# " 2;
=±±
=±
777e
e
eee
6a52 82.F6
<=>E&J2M,b
jj
_
=++ ''
db
)b
m
e
_eh
+
=−−+
'
''
d_b
(.f2M,b
bjbdjdbjdbjd
_
=++−++⇔=++++−⇔ ''''''''
+=+
−=+
⇔
j
j
''
''
=
−
=
⇔
_
_
_g
'
'
7O&6"#D,<M
_='
'
_
_g−
='
7
)b
b_edbhdb_ehdm −−+=−−+⇔ ''''
b_ehb7d_ehdb_ehdm −++−−+=−−+⇔ ''''''
=⇔
=−++
=−−+
⇔ _
_eh
_eh
'
''
''
Nhn xt:<*"IQP?5;
JA
j+= '
2;
=+
=−
j
j
_
_
'
'
#\0b/0
3 8;
bbdd =−−+ ''
6a5. 8'6
<]GU>FIQP+;
'' =++
_
6
<*"IMPR>5,>;
IMP
( ) ( )
( ) ( )
m
_
__e
b_de
eh
b_dh
m
_
__eeh
−
=
+−
−
−
++
−
⇔
−
=−−−−+⇔
'
'
'
'
''
''
=
+−++
−+−−
=
⇔
dib
m
b__ebdehd
h_e
_
''
''
'
7OOdibrd.
b
e
_
≥'
3I<P!2.6
<=>F&J2)*,/M
,b
h
bd
_
_
−>
++
'
'
'
db )b
_e_bed
__
≥−−− ''''
d_b
(.f2M
,bKM
−≥'
7
iO(Sk,*6)*/":7
iO(S≠
≠+−⇒ '
7A$8$Q'%4,),"$M
nehbdh
b7dbd
bd
_
__
__
<⇔<+⇔−>+−⇔−>
+−++
+−
'''''
''
''
7
O&6<4,)*"#M
bnps−=)
)b,Sa,P$M
M
__e_
_
=⇔=−− '''
O
_
−='
H"D)/":7
_M^
e
_
e
_
_
e
_e_
_
_
≥−<⇔
≥≤
>−<
⇔
≥−
>−−
⇔ *''
*''
*''
''
''
7
O&6<4,)"#M
bpest_uv
_
pd +∞∪∪−−∞=)
7
Qua v d trên, lưu cho hc sinh cc đim sau:
<=/>IMPW,!Vc 0W8Q# -++4..V
WA/5!&6
<75#0.-/A0F
/.?5'> d 8F? 690
'> d 8F?..-?+.
W86
<=>&"M
e_
_
+=−+ '.''
D,<)<7
(.f2M
=−−+
≥
⇔
dibhb_d
_
'.'
'
7
dib/D,<M
_
nh_
p
_
nh_
_
_
_
<
+−−−
=>
+−+−
=
'
'
7
"#D,<
dib⇔
D,<)<
−≥
7_
nhbhd
h
nhh
__
_
_
≤⇔
+−≥−
≤
⇔+−≥−⇔−≥⇔ .
.
'
O&6
_≤.
T]57
"/01234/549G;H24/>&
-I23&
bdd =
'(e
"G A;
'( bd=
I0f5
,2
b≥
?eIPSN#5. 8
7'⇒
)/GWAG;
7bdbd =++ '('(
<=>&J2,/M
,b
e
__
=++ ''
)b
'''' eeb_bdmd
_
+=−+
(.f2M
,b;M
_
+= '
≥
7K"D"#QM
7mllh_
__
±=⇔=+⇔=⇔=−+ ''
)b
eee
__
=−+−+⇔ ''''
;M
'' e
_
+=
≥
7"#QM
7
_
ge
_mememe
___
±−
=⇔=−+⇔=+⇔=⇔=−− '''''
<=>?&
.
",/D<M
7_m__
___
.''.'' =−−++
(.f2M;M
vlpsbdl_m
__
∈⇒+−=−−= '''
'
__
m_ '' −=+
7
K"D"#QM
mdibm_
__
±=⇔=−+− .
"#D<
dib⇔
D<
vlps∈
,6M
+≤≤
−≤≤−
⇔
≤−≤
≤+≤
mlm
mlm
lm
lm
.
.
.
.
7
-I23?&
7bvdbdsbdb7d_vbdbds =+++±± ''(''(''(.
*"G A;
7bdbd ''( ±=
$0g?h 8
i G+8R+G?IP 4
IP "6
<=>@&?M
7blbdedle ''.'' −++=−++
,bJ2H
e=.
7
)b
.
""#D<7
(.f2M;M
_gle
_
+=⇒−++= ''
blbded '' −+
dib7
w.^?,DM
gblbded_ ≤−+ ''
8[dib
7_ee ≤≤⇒
"#QM
.
. _g_
_
g
_
_
−=−−⇔
−
+=
bd
,bO(
e=.
,DM
ee_
_
=⇔=−−
,6'
dib
,"$M
=
−=
⇔=−+
l
e
blbded
'
'
''
7
)b"#D<
bd⇔
D<
v_epes∈
7
xaM
g_bd
_
−−= (
'(
v_epes∈
,*6
bd(
"y)%
v_epes_lgb_edbdbedl ∈∀−=≤≤=−⇒ (((
7
c'&6
bd
D<
7e
_
g_l
_lg_lv_epes ≤≤
−
⇔−≤−≤−⇔∈
O&6M
. vep
_
g_l
s
−
∈
T]57
Qua v d trên, lưu cho hc sinh đim sau:
90.'> d3]>d+j
,'( =bd
2.3]
7j, ∈⇔
<=>A&J2M
lbbde_d_ee_ −+++=+++ '''''
(.f2MKM
−≥'
;M
e_ ≥+++= ''
dibhbbde_d_e
_
++++=⇒ '''
K"DQM
m__
__
=⇔=−−⇔−=
,6
m
=
'dib,"$M
em__e_
_
++=− '''
++=+−
≤≤−
⇔
__ng_lhh
j
__
''''
'
=+−
≤≤−
⇔
h_ghl
j
_
''
'
e=⇔ '
<4,"#7
-I23@&
bbdbdd =
''(e
"D
bd'(
3"@*)&
,
7
O(.6,Sa,P$M
M
bd ='
Sa9%7
_M
bd ≠'
,,'%
bd'
,
'";
'
'(
bd
bd
=
,"$
bd
=e
",+)&
,
7
,P;.M
7bdbd7bd7bd7 =++ ''(''(
<=>B&J2M
b_d_m
_e
+=+ ''
7
J2M
−≥
'
7,DM
bd_bd_bbddm
__
+++−=+−+⇔ ''''''
_
m
_
__
=+
+−
+
−
+−
+
⇔
''
'
''
'
dc
b7
_
''' ∀>+−
;M
_
≥
+−
+
=
''
'
,DM
=
=
⇔=+−
_
_
_m_
_
7
i
Memhh
_
_
_
=+−⇔=
+−
+
⇔= ''
''
'
'<7
i
_
ejm
em
h
_
_
_
±
=⇔=−−⇔=
+−
+
⇔= '''
''
'
Ch! :)//>#? /iBC,> ?+.
5/>\ h. 8+W56^YG':EC
;
<=>C&J2M
7he__
__
++=−++ '''''
(.f2M;M
____
ehe__ ''''' −=++⇒−=+=
QM
e
____
=−−⇔−=+
_
_
m
_
_
m
_
−
+
=+⇔
+
=⇔ '''
7
J26,"$<
_
m+
='
'"6<./6*4,
"#7
<=>D&
.
",/D<M
h
_
_e −=++− ''.'
dKz>_jb
(.f2MKM
≥'
i
='
<
7=⇔ .
i
≠'
,,'%
h
_
−'
,"$M
_
e
hh
=
−
+
+
+
−
'
'
.
'
'
7
;M
_
hh
>∀<<⇒
+
−=
+
−
=
''
'
'QM
.
.
−=−⇔=+ _e_e
_
dib
7
"#D<
dib⇔
D<
bpd∈
O
dibbpd_e
e
_
⇒∈∀<−≤−
D<
bpd∈
7
e
e
≤<−⇔<−≤−⇔
O&6
e
≤<− .
]57
kEC32 A?/@BC+.F
/>6J? 8? ABCE8, A5?
h 8>?',>/# T/
BC\ A6)3#/W8V,!??
h 80>?'.A/#
BC 86J"+/G':G -;
-I23A&
7bdbdb7dbd7 =++ ''(''(
O(.6,D";
bd'( =
H"D,"$ -M
bdbd
_
=++ ''
7,2
6 S S,d+'[,D'[,
DSb8,!.6. ABC,!2 ?7
<=>E&J2M
__bd_
__
−−=−+− '''''
(.f2M;M
_
_
−+= ''
,"$M
hbd_
_
=−−− ''
76
)&,-D
_
bd{ +=∆ '
."D6D,<M
7__ ' −==
i
⇒=
_
7lm___
__
±−=⇔=−+⇔=−+ '''''
i
=+−
≤
⇔−=−+⇔−=
_e
___
_
_
''
'
''''
<6'<7
O&6"#D,<M
l±−='
7
#G;H24/>J5J/KLM0N23375J&
75# !,R ABC+
>.+8>6$@iEF.+8>#g?
/> G/>+8>50/>+8>6
<=>F&J2M
__
_ '' =−+
7
*"/>#?5@>/A AB
C6^>0>,>H..C
E++..6)3#V?8c/;J7'>
dF
≤≤− '
50 U
__
' =−
# Y8c
/Vl 0!+8>5i/6*>
5;
KM
7≤'
;
vps
π
∈= '
7K"DQM
_
__
___
=⇔=−+⇔=−+
d.
b7 ≥
O&6M
_
e
_
±=−±== '
<4,"#7
Nhn xt:
<90
' ≤bd
? A
v
_
p
_
sbd
ππ
−∈= '
#/A A
vpsbd
π
∈= '
6
<90
vpsbd ' ∈
? A
v7
_
psbd
_
π
∈= '
<=>&J2M
bd_bd
_e_e
'''' −=−+
(.f2MKM
7≤'
;M
vps
π
∈= '
7QM
7_bbdd_
ee
=−+⇔=+
_e_
_
7_b
_
d
_e
__
=−−+⇔
−
=
−
−⇔
d
b_ ≤+=
_b__bd_d
_
=⇔=++−⇔
O
_ +−=
7
i
7
_
_
h
h
b
h
d_ ==⇒=⇔=−⇔=
πππ
'
i
−−=−
−≤
⇔−=−+⇔−=
__
_
b_d
_
__
''
'
''
−−−
=⇔
=−+−−
−≤
⇔
_
___
_b_d
_
_
'
''
'
9/>EC3#>/33 >">5
,> ?? 0#/> 8,2.,
5/>6)':EC;
<=>&J2M
'''' −+=−+
e
_
_
db
(.f2MKM
≤≤ '
J?5m5+/G_6^i>
/ ?+/G_nJ 43+l 006*
0F T/+!,! 30 8
6
( )
___
_
_
_
_bd
g
h
e
h
e
_
bd '''''''''' −+=−+−+⇔−+=
−+⇔
(
)
==
⇔
=−
=−
⇔=−−−⇔=−−−⇔
*9
*''
''
''
''''''''
_
e
e_ebd_
_
_
____
K%$'("=/H<,D<4,MSk'Sk7
|/,P28,*6"$
_
'' −
)/.}"$\/,
'' −+
P'
"@ +
( )
_
_
_ '''' −+=−+
dib7 ? %/ , ";
'' −+=
_
_
_
−
=−
''
'H"D"#Q)&,'(-
M
=
=
⇔=+−⇔=
−
+
_
_e
e
_
_
O&6,DM
=
=
⇔
=−
⇔
=−+
=−+
_
_
_
'
'
*9
''
''
''
*20?
'' −+
@.B."+
IBCP+.l
//o36J? 8> ABCE85. 8
.+32i> 8./#/W8
+ YI<P6
9/#R.2,>i>?./
;
( ) ( )
__
=−+=−+ ''''
I<P6JYV+3[ 02
5/.V T0n^XYh5+W 8
+ Y+8>;
__
=+
αα
6Jp 0>5;
;M
∈=
_
p
_
π
'
7d=/6$E'
[ ]
p∈'
b7
K"D"#QM
be_dbbddbdde7
e
_
=−+−+−⇔+=+
=
=
⇔
=+−
=
⇔
+−=−
=⇒=
⇔
bnlhd
b_ede
_
'
'
'
'
kEC3#> ?5
!&6> .c[# +.>+/G_
T/. T0>56
OPQR&
')*'C32H%+"HD"
'(!(D8')&D/P;
"=!>?,"@7O'&6"65"$=/56\/,
7\/.6!('&!(_56
PC~!)"#/3.'8/2
+[.,/•)P:,3'&Sa'
8/,5P;" D8H<')%'&."
2)&97€8"'(!(_%"
< .')*'CP
;7A, \/ '()'=')*
'C"=!'?,"@p"yP)R/3
.)&,'(=/2H,/7O('&6",
!('!(_"#D"$HU022)&'=5
6)%&.1)%",3,6)*
'C'=.\/ /3"#)%27
O)&
')*'C33./\/,!
(D8')&D/7O'&6)2*
:!H.656!7
8"63H<4,)2H.6')*
'C!7W;.5/)2*GF!L
G@)'%F=/%56DZ'
)/7
.ST
b IH,)2',>9'5a>/C7
_b ^!/R•>9'5a>/C7
eb ?"=!>?,"@07
hb ,(>,/6K2>9'5a>/C6
mbA/6}],‚,,Kƒ|/2A,
U"SVV
>>>c&d>>>
N 8"= ,
NN ;'*"= ,
NNN ?QE/& ,
NO ?Q9} ,_
O A3./ ,_
ON K%\/28+/ ,_
ONN K%/& ,e
ONNN K%] ,e
Nx </,H2 ,h
x W ,m
