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i s 8 Trn S Tng

I. M U V PHNG TRNH

VN I. Chng minh mt s ! nghi"m #$% mt &h'(ng t)*nh

Phng php: Dng mnh sau:x0 l nghim ca phng trnh A x B x( ) ( )= A x B x0 0( ) ( )=

x0 khng l nghim ca phng trnh A x B x( ) ( )= A x B x0 0( ) ( )

+!i ,. Xt xem x0 c l nghim ca phng trnh hay khng?

a) x x3(2 ) 1 4 2 + = ; x0 2= b) x x5 2 3 1 = + ; x03

2=

c) x x3 5 5 1 = ; x0 2= d) x x2( 4) 3+ = ; x0 2=

e)x x

7 3 5 =

; x0 4

= ) x x2( 1) 3 8

+ = ; x0 2

=g) x x5 ( 1) 7 = ; x0 1= h) x x3 2 2 1 = + ; x0 3=

+!i -. Xt xem x0 c l nghim ca phng trnh hay khng?

a) x x x2 3 7 1 2 + = + ; x0 2= b) x x2 3 10 0 = ; x0 2=

c) x x x2 3 4 2( 1) + = ; x0 2= d) x x x( 1)( 2)( 5) 0+ = ; x0 1=

e) x x22 3 1 0+ + = ; x0 1= ) x x x24 3 2 1 = ; x0 5=

+!i . !m gi" tr# k$a% ch% phng trnh c nghim x0 &'c ch( ra

a) x k x2 1+ = ; x0 2= b) x x k x(2 1)(9 2 ) 5( 2) 40+ + + = ; x0 2=

c) x x x k2(2 1) 18 3( 2)(2 )+ + = + + ; x0 1= d) k x x x 5( 3 )( 1) 4(1 2 ) 80+ + + = ; x0 2=

VN II. / nghi"m #$% mt &h'(ng t)*nhPhng php: Dng mnh sau:

Phng trnh A x B x( ) ( )= v nghim A x B x x( ) ( ), Phng trnh A x B x( ) ( )= c v s nghim A x B x x( ) ( ),=

+!i ,. *h+ng t, c"c phng trnh $a- . nghima) x x x2 5 4( 1) 2( 3)+ = b) x x2 3 2( 3) =

c) x 2 1 = d) x x2 4 6 0 + =+!i -. *h+ng t, r/ng c"c phng trnh $a- c . $0 nghim

a) x x x4( 2) 3 8 = b) x x4( 3) 16 4(1 4 ) + = +c) x x2( 1) 2 2 = d) x x=

e) x x x2 2( 2) 4 4+ = + + ) x x x2 2(3 ) 6 9 = =+!i . *h+ng t, r/ng c"c phng trnh $a- c nhi1- hn m2t nghim

a) x2 4 0 = b) x x( 1)( 2) 0 =

c) x x x( 1)(2 )( 3) 0 + = d) x x2

3 0 =e) x 1 3 = ) x2 1 1 =

VN III. Chng minh h%i &h'(ng t)*nh t'(ng 0'(ng

CHNG III1 PHNG TRNH +2C NHT M3T 4N

!rang 34

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i s 8 Trn S Tng

"# ch$ng minh hai phng trnh tng ng% ta c th# s& '(ng m)t tr*ng cc cch sau:+h$ng minh hai phng trnh c cng t,p nghim-.& '(ng cc ph/p 0i1n 2i tng ng # 0i1n 2i phng trnh n3 thnh phng trnh kia-4ai 5ui t6c 0i1n 2i phng trnh:

7 Qui tc chuyn v: !r*ng m)t phng trnh% ta c th# chuyn mt hng t t v ny sangv iav !"i #$uh8ng t& -

7 Qui tc nh%n: !r*ng m)t phng trnh% ta c th# nh%n c& hai v v'i cng mt s h(c )-

+!i ,. Xt xem c"c phng trnh $a- c tng &ng hay khng?a) x3 3= . x 1 0 = b) x 3 0+ = . x3 9 0+ =c) x 2 0 = . x x( 2)( 3) 0 + = d) x2 6 0 = . x x( 3) 0 =

+!i -. Xt xem c"c phng trnh $a- c tng &ng hay khng?

a) x2 2 0+ = . x x2( 2) 0+ = b) x x1+ = . x2 1 0+ =

c) x 2 0+ = .x

x0

2=

+d) x x

x x

2 1 1+ = + . x x2 0+ =

e) x 1 2 = . x x( 1)( 3) 0+ = ) x 5 0+ = . x x2( 5)( 1) 0+ + =

II. PHNG TRNH +2C NHT M3T 4N

!rang 35

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Trn S Tng i s 8

VN I. Ph'(ng t)*nh 0'% 0'5# 67 89ng &h'(ng t)*nh :;# nh. 6i7i c"c phng trnh $a-

a)x x x2 1 2 7

5 3 15

+ = b)

x x x3 1 51

2 3 6

+ + = +

c)x x x x2( 5) 12 5( 2)

113 2 6 3

+ + + = + d)

x x x xx

4 3 2 2 5 7 2

5 10 3 6

++ =

e)x x x2( 3) 5 13 4

7 3 21

++ = )

x xx

3 1 1 4 9

2 4 8

=

".: a9 < tu= > 09 < tu= > c9 < tu= > '9 v nghim 9 v nghim ;9 v nghim

+!i ?. 6i7i c"c phng trnh $a-

!rang 33

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i s 8 Trn S Tng

a)x x x x x x( 2)( 10) ( 4)( 10) ( 2)( 4)

3 12 4

+ + + + = b) x xx

2 2( 2) ( 2)

2(2 1) 258 8

+ + = +

c) x x x x2 2

(2 3)(2 3) ( 4) ( 2)

8 6 3

+ = + d)

x x x x2 2 27 14 5 (2 1) ( 1)

15 5 3

+ =

e)

x x x x x2(7 1)( 2) 2 ( 2) ( 1)( 3)

10 5 5 2

+ + = +

".: a9 x 8= 09 x 9= c9 x 123

64= '9 x

1

12= 9 x

19

15=

+!i @. 6i7i c"c phng trnh $a- 8?i1n 2i @c 0it)

a)x x x x1 3 5 7

35 33 31 29

+ + + ++ = + 84D: +)ng thAm B v* cc h8ng t&)

b)x x x x x10 8 6 4 2

1994 1996 1998 2000 2002

+ + + + = 84D: !rC i B v* cc h8ng t&)

x x x x x2002 2000 1998 1996 1994

2 4 6 8 10

= + + + +

c)x x x x x1991 1993 1995 1997 1999

9 7 5 3 1

+ + + + =

x x x x x9 7 5 3 1

1991 1993 1995 1997 1999

= + + + + 84D: !rC i B v* cc h8ng t&)

d)x x x x85 74 67 64

1015 13 11 9

+ + + = 8+h >: 10 1 2 3 4= + + + )

e)x x x x1 2 13 3 15 4 27

13 15 27 29

= 84D: !hAm h*@c 0Et B v* cc h8ng t&)

".: a9 x 36= 09 x 2004= c9 x 2000= '9 x 100= 9 x 14= -+!i A. 6i7i c"c phng trnh $a- 8?i1n 2i @c 0it)

a)x x x x1 3 5 7

65 63 61 59

+ + + ++ = + b)

x x x x29 27 17 15

31 33 43 45

+ + + + =

c)x x x x6 8 10 12

1999 1997 1995 1993

+ + + ++ = + d)

x x x x1909 1907 1905 19034 0

91 93 95 91

+ + + + =

e)x x x x x x29 27 25 23 21 19

1970 1972 1974 1976 1978 1980

+ + + + + =

x x x x x x1970 1972 1974 1976 1978 1980

29 27 25 23 21 19

= + + + + +

".: a9 x 66= 09 x 60= c9 x 2005= '9 x 2000= 9 x 1999= -

VN II. Ph'(ng t)*nh tB#h

!rang 39

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Trn S Tng i s 8

"# giFi phng trnh tGch% ta p '(ng cng th$c:

A x B x A x( ). ( ) ( ) 0 = h*@c B x( ) 0= A xB x

( ) 0

( ) 0

= =

!a giFi hai phng trnh A x( ) 0= v B x( ) 0= % rHi lI3 tIt cF cc nghim ca chng-

+!i ,. 6i7i c"c phng trnh $a-a) x x(5 4)(4 6) 0 + = b) x x(3,5 7)(2,1 6,3) 0 =c) x x(4 10)(24 5 ) 0 + = d) x x( 3)(2 1) 0 + =e) x x(5 10)(8 2 ) 0 = ) x x(9 3 )(15 3 ) 0 + =

".: a9x x4 3

;5 2

= = 09 x x2; 3= = c9 x x5 5

;2 24

= = '9 x x 1

3;2

= =

9 x x2; 4= = ;9 x x3; 5= = +!i -. 6i7i c"c phng trnh $a-

a) x x2(2 1)( 2) 0+ + = b) x x2( 4)(7 3) 0+ =

c) x x x2

( 1)(6 2 ) 0+ + = d) x x x2

(8 4)( 2 2) 0 + + =".: a9x

1

2= 09 x

3

7= c9 x 3= '9 x

1

2=

+!i . 6i7i c"c phng trnh $a-a) x x x( 5)(3 2 )(3 4) 0 + = b) x x x(2 1)(3 2)(5 ) 0 + =c) x x x(2 1)( 3)( 7) 0 + = d) x x x(3 2 )(6 4)(5 8 ) 0 + =e) x x x x( 1)( 3)( 5)( 6) 0+ + + = ) x x x x(2 1)(3 2)(5 8)(2 1) 0+ =

".: a9 S 3 45; ;

2 3

=

09 S

1 2; ; 5

2 3

= =

c9 S

1;3; 7

2

=

'9 S

3 2 5; ;

2 3 8

=

9 { }S 1; 3; 5;6= ;9 S 1 2 8 1; ; ;2 3 5 2 = +!i =. 6i7i c"c phng trnh $a-

a) x x x x( 2)(3 5) (2 4)( 1) + = + b) x x x x(2 5)( 4) ( 5)(4 )+ =

c) x x x29 1 (3 1)(2 3) = + d) x x x x22(9 6 1) (3 1)( 2)+ + = +

e) x x x x2 227 ( 3) 12( 3 ) 0+ + = ) x x x x216 8 1 4( 3)(4 1) + = +

".: a9 x x2; 3= = 09 x x0; 4= = c9x x1

; 23

= = '9x x1 4

;3 5

= =

9 x x x 4

0; 3;

9

= = = ;9 x 1

4

=

+!i >. 6i7i c"c phng trnh $a-

a) x 2(2 1) 49 = b) x x2 2(5 3) (4 7) 0 =

c) x x2 2(2 7) 9( 2)+ = + d) x x x2 2( 2) 9( 4 4)+ = +

e) x x2 24(2 7) 9( 3) 0+ + = ) x x x x2 2 2 2(5 2 10) (3 10 8) + = +

".: a9 x x4; 3= = 09 x x 10

4;9

= = c9 x x 13

1;5

= = '9 x x1; 4= =

9 x x 23

5;7

= = ;9 x x 1

3;2

= =

+!i ?. 6i7i c"c phng trnh $a-a) x x x x2 2(9 4)( 1) (3 2)( 1) + = + b) x x x x2 2( 1) 1 (1 )( 3) + = +

c) x x x x x x2 2( 1)( 2)( 3) ( 1)( 4)( 5) + = + d) x x x4 3 1 0+ + + =

!rang 3:

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i s 8 Trn S Tng

e) x x3 7 6 0 + = ) x x x4 34 12 9 0 + =g) x x x5 35 4 0 + = h) x x x x4 3 24 3 4 4 0 + + =

".: a9x x x2 1

; 1;3 2

= = = 09 x x1; 1= = c9 x x x 7

1; 2;5

= = =

'9 x 1= 9 x x x1; 2; 3= = = ;9 x x1; 3= =

g9 x x x x x0; 1; 1; 2; 2= = = = = h9 x x x1; 1; 2= = =+!i @. 6i7i c"c phng trnh $a- 8"@t Jn ph()

a) x x x x2 2 2( ) 4( ) 12 0+ + + = b) x x x x2 2 2( 2 3) 9( 2 3) 18 0+ + + + + =

c) x x x2( 2)( 2)( 10) 72 + = d) x x x x2( 1)( 1) 42+ + + =

e) x x x x( 1)( 3)( 5)( 7) 297 0 + + = ) x x x4 22 144 1295 0 = ".: a9x x1; 2= = 09 x x x x0; 1; 2; 3= = = = c9 x x4; 4= = '9 x x2; 3= =

9 x x4; 8= = ;9 x x5; 7= =

VN III. Ph'(ng t)*nh #h% n D mEF+c 0Ec giFi phng trnh ch$a Jn K mLu:

*+'c ,-!m iu kin

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Trn S Tng i s 8

a)x

x xx x26 1 5 3

2 57 10

++ =

+b)

x x

x x x xx22 1 4

0( 2) ( 2)4

+ =

+

c)x x

x x x x x

2

2

1 1 ( 1)

3 1 3 2 3

=

+ d)

x x x x21 6 5

2 3 6 =

+

e)x

x x x x

2

3 2

2 2 16 5

2 8 2 4

+ =+ + + )

x x x

x x x x x

2

2 2 6

1 1 2( 2)

1 1 1

+ + =+ + +

".: a9x 9

4= 09 v nghim c9 x

3

5= '9 x 4=

9 v nghim ;9 x 5

4=

+!i =. 6i7i c"c phng trnh $a-

a)x x x x

8 11 9 10

8 11 9 10+ = +

b)

x x x x

x x x x3 5 4 6 =

c) x x x x2 2

4 31 0

3 2 2 6 1 + = + + d) x x x x1 2 3 6

1 2 3 6+ + =

".: a9 x x 19

0;2

= = 09 x x 9

0;2

= = c9 x x0; 3= = '9 x x6 12

;5 5

= =

+!i >. 6i7i c"c phng trnh $a-a) b)

".: a9

III. GII TN +JNG CCH K2P PHNG TRNH

!rang 3

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i s 8 Trn S Tng

+c 0Ec giFi t*n 0Vng cch l,p phng trnh:*+'c ,-9:; ;h+i&i ;h+- tPng $0 b# chia l=n 54 . gi7m $0 chia &i m2t nHa th hi- ca

hai $0 mAi l 94E !m hai $0 &E".: 3:; CE

+!i >. F2t &2i cng nhGn $Ha m2t &%Qn &Rng tr%ng 9 ngyE Jgy th+ nhMt &2i $Ha &'c1

3&%Qn

&Rng ngy th+ hai &2i $Ha &'c m2t &%Qn &Rng b/ng4

3&%Qn &'c lm &'c tr%ng ngy

th+ nhMt ngy th+ ba &2i $Ha C4m cSn lQiE !Tnh chi1- di &%Qn &Rng m &2i ph7i $HaE".: 9t r/ng n>- x%" ch` $0 3 & th $0 My gi7m &i 344E

!rang 3D

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Trn S Tng i s 8

".: 333E+!i ,O.6ia &nh % c : ngRi b0 m b Fai . %E !-Li tr-ng bnh ca c7 nh l 39E J>-

.i>t th=m ch` $0 4 .% b=n ph7i t-Li b Fai th &'c t-Li ca b0 t-Li ca m b/ng9

10t-Li

b0 . gMp 9 l@n t-Li ca %E !m t-Li ca mYi ngRi tr%ng gia &nh %E".: !u2i ca 0% m^% 0/ _ai v "* l[n lQt l: :4 9 &>n bQn c-0i c]ng th+ n nhn n.i=n k% . &'c lMy th=m1

11$0 k% cSn lQiE

U,i phGn &2i & c ba% nhi=- &2i .i=n . mYi &2i .i=n nhn ba% nhi=- .i=n k%E".: 54 )i viAn m`i )i vin nh,n 54viAn k^*-

+!i ,-. F2t ngRi b"n $0 $@- ri=ng th- h%Qch &'c nh $a-

B @n th+ nhMt b"n \ tr"i .1

6$0 $@- ri=ng cSn lQiE

B @n th+ hai b"n 5C tr"i .1

6$0 $@- ri=ng cSn lQi mAiE

B @n th+ ba b" 3D tr"i .1

6$0 $@- ri=ng cSn lQi mAi .E.EEE

Ai c"ch & th b"n l@n $a- c]ng l .Na h>t . $0 $@- ri=ng b"n mYi l@n &1- b/ng nha-EU,i ngRi & &K b"n ba% nhi=- l@n . $0 $@- ri=ng th- h%Qch &'c l ba% nhi=- tr"i?".: 33 tri%0n l[n-

+!i ,.fa lAp j f * gp $"ch tng c"c bQn hc $inh .]ng kh khPn tMt c7 &'c 9C c-0nE !( $0

$0 c-0n $"ch ca lAp j $% .Ai lAp f l6

11E !( $0 $0 c-0n $"ch ca lAp j $% .Ai lAp * l

7

10E

U,i mYi lAp gp &'c ba% nhi=- c-0n $"ch?".: YEp : C: cunb lEp ?: 5: cunb lEp +: 534 cun-

+!i ,=._Gn $0 t(nh j hin nay l

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i s 8 Trn S Tng

. c hai chZ s c '8ng: xy x y10= + - "iu kin: x y N x y, ,0 9,0 9 < -

. c 0a chZ s c '8ng: xyz x y z100 10= + + - "iu kin: x y z N x y z, , ,0 9,0 , 9 < -

+!i ,. !m m2t $0 t nhi=n c hai ch` $0 bi>t r/ngB !Lng hai ch` $0 l 53

B J>- &Li chY hai ch` $0 th &'c m2t $0 mAi lAn hn $0 & l 9- th=m ch` $0 5 .% b=n ph7i hay b=n tr"i $0 & ta &'c m2t

$0 c < ch` $0E fi>t r/ng n>- .i>t th=m .% b=n ph7i $0 & th &'c m2t $0 lAn gMp ba l@n $0nhn &'c khi ta .i>t th=m .% b=n tr"i $0 &E !m $0 &E

".: :3CDE+!i =. F2t $0 c hai ch` $0 tr%ng & ch` $0 hng chc gMp 9 l@n ch` $0 hng &n .#E J>- &Li chY

hai ch` $0 ta &'c m2t $0 c hai ch` $0 nh, hn $0 ban &@- 5C &n .#E !m $0 &E".: 95E

+!i >. F2t $0 t nhi=n c hai ch` $0 c tLng c"c ch` $0 b/ng DE J>- th=m ch` $0 4 .% gi`a haich` $0 ta &'c m2t $0 c 9 ch` $0 lAn hn $0 &K ch% l 5C4E !m $0 &E

".: 3E+!i ?.

".:

VN III. KL9i !m #hFng S !m )ing mt 6i"#Shi cng vic khng Qc * 0Vng s lQng c( th#% ta c*i t*n 0) cng vic l m)t n vMcng vic% 0i#u thM 0Ki s B-dng suIt lm vic l ph[n vic lm Qc tr*ng m)t n vM th\i gian-OWi l khi lQng cng vic% n l ndng suIt% t l th\i gian lm vic- !a c: A nt= -!2ng ndng suIt riAng 0Vng ndng suIt chung khi cng lm-

+!i ,. Uai ngRi c]ng lm m2t cng .ic tr%ng 3: giR th x%ngE JPng $-Mt ca ngRi th+ nhMt b/ng3

2

nPng $-Mt ca ngSi th+ haiE U,i n>- mYi ngRi lm m2t mnh c7 cng .ic th ph7i mMt

thRi gian ba% lG-?".: ef gi\b f gi\-

+!i -. F2t bon ch+a c &t hai .Si nAc ch7y .% . m2t .Si th"% nAc raEB fon tr0ng khng n>- mV ri=ng .Si th+ nhMt th $a- : giR bon &@y nAcEB fon tr0ng khng n>- mV ri=ng .Si th+ hai th $a- < giR bon &@y nAcEB fon tr0ng khng n>- &ong thRi mV c7 ba .Si th $a- D giR 53 phZt bon &@y nAcEU,i n>- bon ch+a &@y nAc mV ri=ng .Si th"% nAc th $a- ba% lG- $ th"% h>t nAc ra?

".: T gi\ T pht-+!i . F2t cng nhGn ph7i lm m2t $0 $7n phqm tr%ng 5C ngyE _% &K .'t m+c mYi ngy $7n

phqm n=n $a- 5< ngy anh &K lm x%ng . lm th=m 34 $7n phqm n`a ng%i k> h%QchE !Tnh

xem mYi ngy anh &K lm &'c ba% nhi=- $7n phqmE".: DsFn phJm-

VN IV. KL9i #hFn 0ng 07F

!rang 3\

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Trn S Tng i s 8

OWi ' l 5uUng \ng )ng t& i% v l v,n tc% t l th\i gian i% ta c: d vt= -,n tc n a &im f .Ai .n t0c 4 km^h roi tN f O-ay ngay .1j .Ai .n t0c :4 km^hE *7 &i . .1 mMt m2t thRi gian l giR 3: phZtE !m chi1- di O-Kng&Rng tN j &>n fE

".: km120 -+!i -. F2t xe &Qp khVi hnh tN &im j chQy .Ai .n t0c 34 km^hE Wa- & 9 giR m2t xe hi &-Li

the% .Ai .n t0c 4 km^hE U,i xe hi chQy tr%ng ba% lG- th &-Li k#p xe &Qp?".: 2gi\-

+!i . F2t ngRi &i xe gn m"y &i tN a &im j &>n a &im f tr=n m2t O-Kng &Rng di km35 EZc trV .1 ngRi & &i the% c%n &Rng kh"c di km42 .Ai .n t0c km hn .n t0c l't &i l

< km^hE !hRi gian l't .1 b/ng3

2thRi gian l't &iE !m .n t0c l't &i . l't .1E

".: ,n tc lQt i l Tf kmhb v,n tc lQt v l e kmh-

+!i =. F2t xe t7i &i tN j &>n f .Ai .n t0c 4 km^hE i &'c 3: phZt th gp &Rng xM- n=n .nt0c tr=n O-Kng &Rng cSn lQi gi7m cSn :4 km^hE .y &K &>n ni chm mMt 5C phZtE !mchi1- di O-Kng &Rng tN j &>n fE

".: km80 -+!i >. Zc < giR 5 phZt m2t t &i tN j & &=n f .Ai .n t0c D4 km^hE hi &>n f t ngh( 5 giR

rsi roi O-ay .1 j .Ai .n t0c n j lZc 55 giR c]ng ngyE !Tnh O-Kng &RngjfE

".: 54km-+!i ?. Ung ngy !-Mn &i xe &Qp &>n trRng .Ai .n t0c 53 km^hE W"ng nay d% dy m-2n !-Mn

x-Mt ph"t chm 3 phZtE !-Mn nhqm tTnh & &>n trRng &Zng giR nh hm trAc th !-Mn ph7i&i .Ai .n t0c 5 km^hE !Tnh O-Kng &Rng tN nh !-Mn &>n trRngE

".: 3 km-+!i @. F2t ngRi &i xe m"y tN thnh ph0 !hanh U%" . thnh ph0 inhE J>- chQy .Ai .n t0c 3

km^h th $ m-2n $% .Ai d nh l 3 giRE J>- chQy .Ai .n t0c 94 km^h . gi`a &Rng ngh( 5giR th cng m-2n mMt 3 giRE U,i & &>n ni &Zng giR m dc &Rng khng ngh( th xe ph7ichQy mYi giR ba% nhi=- kilmet?

".: 9D km-+!i A. Uai t khVi hnh c]ng m2t lZc & &i tN U-> . JungE n t0c xe th+ nhMt l :4 km^h

.n t0c xe th+ hai l n Jung ngh( nHa giR roi O-ay lQi U-> th gpxe th+ nhMt V c"ch Jung 54 kmE !Tnh O-Kng &Rng U-> v JungE

".: 554 km-

+!i . w-Kng &Rng j_ di \ km gom &%Qn jf l=n d0c &%Qn f* n/m ngang &%Qn *_ x-0ngd0cE F2t ngRi &i b2 tN j &>n _ roi O-ay trV .1 j h>t tMt c7 9 giR :5 phZtE !Tnh O-Kng &Rngf* bi>t .n t0c lZc l=n d0c ca ngRi & l : km^h lZc x-0ng d0c l < km^h . lZc &i tr=n&Rng n/m ngang l km^hE

".: :km-+!i ,O.F2t xe t7i &i tN j &>n f .Ai .n t0c : km^hE Wa- & m2t thRi gian m2t xe c%n cng x-Mt

ph"t tN j .Ai .n t0c - khng c g thay &Li th &-Li k#p xe t7i tQi fE Jhng $a-khi &i &'c nHa O-Kng &Rng jf th xe c%n tPng .n t0c l=n D km^h n=n $a- & 5 giR th&-Li k#p xe t7iE !Tnh O-Kng &Rng jfE

".: :4 km-+!i ,,. F2t &S m"y x-i dSng tN b>n j &>n b>n f mMt : giR . ng'c dSng tN f .1 j mMt giRE

n t0c ca dSng nAc l 3 km^hE !m chi1- di O-Kng &Rng tN j &>n fE".: km80 -+!i ,-.F2t ca n x-i dSng tN j &>n f mMt giR . ng'c dSng tN f &>n j mMt < giRE !Tnh

kh%7ng c"ch jf bi>t .n t0c dSng nAc l 3 km^hE

!rang 94

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i s 8 Trn S Tng

".: 534 km-+!i ,.Uai b>n $ng j . f c"ch nha- :4 kmE *]ng m2t lZc .Ai ca n x-i dSng tN b>n j c m2t

chi>c b tri tN b>n j .Ai .n t0c 9 km^hE Wa- khi &>n f ca n trV .1 b=b$ j ngay . gp bkhi b &K tri &'c C kmE !Tnh .n t0c ca ca nE

".: 3D kmh-+!i ,=.F2t chi>c th-y1n &i tN b>n j &>n b>n f h>t giR tN b>n f &>n b>n j h>t D giRE U,i m2t

&"m b% tri the% dSng $ng tN j &>n f h>t ba% lG-?".: 9gi\-+!i ,>.

".:

VN V. KL9i #W ni 8Fng h*nh hX#4nh chZ nh,t c hai kGch thEc a% 0- Din tGch: S ab= b +hu vi: P a b2( )= +

!am gic vung c hai c8nh gc vung a% 0- Din tGch: S ab1

2=

+!i ,. *h- .i m2t kh- .Rn hnh ch` nht b/ng m60 hi- &2 di ca chi1- di . chi1- r2ng lm20 E !m &2 di c"c cQnh ca hnh ch` nhtE

".: m m5 ;25 -+!i -. F2t thHa &Mt hnh ch` nht c ch- .i l m56 E J>- gi7m chi1- r2ng m2 . tPng chi1- di

m4 th din tTch tPng th=m m28 E !m chi1- r2ng . chi1- di thHa &MtE

".: m m12 ;16 E+!i . F2t kh- .Rn hnh ch` nht c chi1- di b/ng 9 l@n chi1- r2ngE J>- tPng mYi cQnh th=m

m5 th din tTch kh- .Rn tPng th=m m2385 E !Tnh &2 di c"c cQnh ca kh- .RnE".: m m18 ;54 E

+!i =. Ui- $0 &% ch- .i ca hai hnh .-ng l m32 . hi- $0 &% din tTch ca chZng l m2464 E!m $0 &% c"c cQnh ca mYi hnh .-ngE

".: c8nh hnh vung nh l m25 b c8nh hnh vung lEn l m33 -

+!i >. F2t kh- .Rn hnh ch` nht c ch- .i l m450 E J>- gim chi1- di &i1

5chi1- di c .

tPng chi1- r2ng th=m1

4chi1- r2ng c th ch- .i hnh ch` nht khng &LiE !Tnh chi1- di .

chi1- r2ng kh- .RnE".: m m100 ;125 E+!i ?. F2t kh- &Mt hnh ch` nht c chi1- di hn chi1- r2ng l 54mE J>- chi1- di tPng th=m

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Trn S Tng i s 8

+!i ,. 6i7i c"c phng trnh $a-

a) x x x x x26 5 3 2 3 (3 2 ) + = b)x x x

x2( 4) 3 2 1

4 10 5

+ = +

c)x x x2 3 5 3(2 1) 7

3 4 2 6

+ = d)

x x xx

6 5 10 3 2 12

2 4 2

+ + + = +

e) x x x x 2( 4)( 4) 2(3 2) ( 4) + = ) x x x x3 3 2( 1) ( 1) 6( 1)+ = + +

".: a9 x 3

2= 09 x 5= c9 x

17

19= '9 x

1

2= 9 x 14= ;9 x

2

3=

+!i -. 6i7i c"c phng trnh $a-

a) x x x x(4 3)(2 1) ( 3)(4 3) = b) x x x225 9 (5 3)(2 1) = + +

c) x x2 2(3 4) 4( 1) 0 + = d) x x x x4 3 22 3 8 4 0+ =

e) x x x2( 2)( 2)( 10) 72 + = ) x x x3 22 7 7 2 0+ + + =

".: a9 S 3

; 24

= 09 S 3 4

;5 3

= c9 S

2

;65

= '9 { }S 1; 2;2=

9 { }S 4;4= ;9 S 1

2; 1;2

=

+!i . 6i7i c"c phng trnh $a-

a)x x x x2 4 6 8

98 96 94 92

+ + + ++ = + b)

x x x x2 2 45 3 8 4 69

13 15 37 9

+ + + ++ = +

".: a9 x 100= 09 x 15= +!i =. 6i7i c"c phng trnh $a-

a)x x x2

2 3 4

2 1 2 1 4 1

=+

b)x x

x xx x2

2 18 2 5

1 32 3

+ =

+ ++

c)x

x x x x

2

3 2

1 2 5 4

1 1 1

+ =

+ +

".: a9 x 9

2= 09 x 1= c9 x 0=

+!i >. !hng ca hai $0 b/ng 9E J>- tPng $0 b# chia 54 &n .# . gi7m $0 chia &i m2t nHa th $0th+ nhMt th- &'c lAn hn $0 th+ hai th- &'c l 94E !m hai $0 ban &@-E

".: 3: vCE+!i ?. *h- .i ca m2t hnh ch` nht b/ng 5:4 m hi- gi`a $0 &% chi1- di . chi1- r2ng l 54 mE

!m $0 &% c"c cQnh ca hnh ch` nhtE".: 94 m v :4 mE

+!i @. !h]ng th+ nhMt &ng :4 lTt d@- th]ng th+ hai &ng C lTt d@-E th]ng th+ hai lMy ra m2tl'ng d@- gMp 9 l@n l'ng d@- lMy ra V th]ng th+ nhMtE Wa- & l'ng d@- cSn lQi tr%ng th]ngth+ nhMt gMp &i l'ng d@- cSn lQi tr%ng th]ng th+ haiE U,i &K lMy ra ba% nhi=- lTt d@-?

".: 3< lGt v DC lGt-+!i A. *h- .i b"nh xe lAn ca m2t &@- m"y xe lHa l < m . ca b"nh xe nh, l 3: mE hi xe

chQy tN ga j &>n ga f th b"nh nh, &K lPn nhi1- hn b"nh lAn l :444 .SngE !Tnh O-Kng&Rng jfE

".: 5

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i s 8 Trn S Tng

&@- .Ai .n t0c hn d nh l 54 kmh. &i nHa O-Kng &Rng cSn lQi .Ai .n t0c thMp hnd nh l < kmhnhng t &K &>n &Zng thRi gian &K nhE !Tnh thRi gian t &K d nh &iO-Kng &Rng tr=nE

".: 3gi\E+!i ,,. F2t xe t &i tN U J2i .1 !hanh U%"E Wa- khi &i &'c :9 km th dNng lQi :4 phZtE .1

&>n !hanh U%" &Zng giR &K nh n ph7i &i .Ai .n t0c b/ng 53 l@n .n t0c trAc &E !Tnh

.n t0c lZc &@- bi>t r/ng O-Kng &Rng U J2i v !hanh U%" di 5