- - 2011.

1

( ) ( )n nf x b a af x b ,a b R (1).

( ) ( ( ) ) ( ) ( )nng x af x b g x b af x (2).

( ) ( )n nf x b ag x (3)

( ) ( )

( ) ( )

n

n

g x b af x

f x b ag x

.

.

.

:

:3 31 2 2 1x x .

2, 1, ( )a b f x x .

33y 2x 1 y 1 2x .

V y ta có h :

3

3

x 1 2y

y 1 2x

. Tr ủa h :

3 3 2 2x y 2(y x) (x y)(x xy y 2) 0 x y

(Do 2 2 2 2y 3

x xy y 2 (x ) y 2 02 4

) Thay vào h ta có:

3 3 2x 1 2x x 2x 1 0 (x 1)(x x 1) 0

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2

x 1

1 5x

2

. V m: 1 5

x 1;x2

.

2 3

2 42

xx x

, , ( )a b f x .

( )f x .

. ( )f x .

Ta 2 22 4 2( 2 )x x x x =

2 2 22 4 2( 2 1) 2 2( 1) 2x x x x x .

( )f x = .

( )f x

2 (x 1) 22(x 1) 2

2

2 1 x 1(x 1) 1 1

2 2

.

1

2, .

t

2 ty 1x 1 t

t x 1; y 1 1 22 2

y 0

.

Ta có h :

2

2

1t 1 y

2

1y 1 t

2

t y1

(t y)(t y ) 0 12 y t

2

*

2 2tt 1 2t t 2 0

t y 2t 0t y 0

1 17 3 17

t x4 4

(th a x 3 ).

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3

*

2 21 t(t ) 1 4t 2t 3 0

1 2 2y t 112 tt 22

1 13 5 13t x

4 4

(th x 3 ).

V m: 3 17 5 13

x ;x4 4

.

Gi 2x x 1000 1 8000x 1000 .

1

x8000

2 1000 1000 1 8000x x x .

( )f x .

.

PT24x 4x 4000 4000 4000(2x 1) 3999

2(2x 1) 4001 4000 4000(2x 1) 4001 ( )f x = 2 1, 4000, 4001x a b ).

t u 2x 1; v 1 8000x ; 4001

v 0,u4000

, ta có h

2 2

2 2 2

u 4001 4000v u 4001 4000v

v 4001 4000u u v 4000(v u)

2u 4001 4000v (1)

(u v)(u v 4000) =0 (2)

. Do u v 4000 0 nên T (2) ta có:

u v c:2u 4000u 4001 0

u 0

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4

u 4001 x 2001 . V m: x 2001 .

, , ( )a b f x .

,a b do

.

Gi 24x 7x 1 2 x 2 .

( )f x a =2).

2 24 (2 )x x 2( ) (2 )f x x c c .

( )f x o.

2(2x 1) 3x 2 2(2x 1) 3x . .

t 2t 2x 1; y 2t 3x y 3x 2t và y 0 .

Ta có :

2

2

t 3x 2y y t(t y)(t y 2) 0

y t 2y 3x 2t

.

*

22 4x 3x 1 0

1t 2t 3x 0y t x1 4t 0 x

2

.

*

22 4x 11x 7 0

t 3x 2(t 2) 0y t 2 3

t 2 x2

7x

4 .

V m: 7 1

x ;x4 4

.

Gi 2 24x 11x 10 (x 1) 2x 6x 2 .

2( ) (2 )f x x c .

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5

c :

2 2 2 2

2

4 4 ( 11 4 ) 10 ( 1) ( 1)(2 ) ( 11 4 ) 10

(11 4 ) 10 .

x cx c c x c x x x c c x c

b c x c

3c .

PT 2(2x 3) x 1 (x 1) (x 1)(2x 3) x 1

t u 2x 3; v (x 1)(2x 3) x 1 ,

Ta có h

2

2

u x 1 (x 1)v

v x 1 (x 1)u

2 2u v (x 1)(v u) (u v)(u v x 1) 0

* 2u v u x 1 (x 1)u 2(2x 3) x 1 (x 1)(2x 3)

22x 6x 7 0 m.

* 2u v x 1 0 2x 3 2x 6x 2 x 1 0

22x 6x 2 4 3x 2

4x

3

7x 18x 14 0

h vô nghi m.

V m.

3 2 233 6 3 17 3 9( 3 21 5)x x x x x .

ủ vn.com.

( ) (3 ) ( )f x x c f x x c

( ) (3 )f x x c .

PT 3 2 2327 54 27 153 27 9( 3 21 5)x x x x x . (*)

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6

Tuy nhiên .

.

. ủ

c b =

). b

= 281x . ủ

227x c 3c . .

3 2 2 23 3(3 3) (27 126 108 ) 27 9( 3 21 5) 27 27(3 3) (27 126 108 )x x x x x x x x .

.

233 3; 27(3 3) (27 126 108 )u x v x x x .

3 2

3 2

(27 126 108 ) 27

(27 126 108 ) 27

u x x v

v x x u

.

33 2 210 2 7 23 12x x x x x .

3 2( ) ( 2) ; 7 22 10, 1f x x b x x a .

3 2 232; 7 23 12 ( 2) ( 7 22 10)u x v x x x x x .

3 2

3 3

3 2

2 2

3 2

2 2 2 2

7 22 10

7 22 10

( )( 1) 0

( 2) 7 23 12(*)

31 0 ( ) 1 0(**)

2 4

u x x vu v v u

v x x u

u v u v uv

x x xu v

vu v uv u v

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7

3 2 2(*) 5 11 4 0 ( 4)( 3 1) 0

4

3 5

2

3 5

2

x x x x x x

x

x

x

3 5 3 5

4; ;2 2

x x x

.

ủ .

.

3 27 23 12x x .

4t x . Thay 3 27 23 12 6x x = t , do 4t

2 . 3 22 7 23 12t x x .

3 2 2

3 2

3 3 2 2 2 2

6 12 7 23 4

10 4

6 6 13 13 0 ( )( 6 6 13) 0

t t t x x

x x x t

t x t x x t t x t x tx t x

.

2 2 6 6 13 0

t x

t x tx t x

3 23 2

22 2

( 2) 7 23 12(*)2 7 23 12

3[( 3) ] 3 4 0(**)( 3) ( 3) 3 4 0

2 4

x x xx x x

xt x xt x t x x

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8

3 2 2(*) 5 11 4 0 ( 4)( 3 1) 0

4

3 5

2

3 5

2

x x x x x x

x

x

x

3 5 3 5

4; ;2 2

x x x

.

a

" "

a " "

B 8: Gi 32 21

8x 13x 7 (1 ) 3x 2x

.

ủ .

33 2 28x 13x 7x (x 1) 3x 2 . (*)

v . v

.

( ) (2 1)f x x

(*) 3 2 23(2x 1) (x x 1) (x 1) (x 1)(2x 1) x x 1

3 2u 2x 1; v 3x 2

Ta

3 22 2

3 2

u (x x 1) (x 1)v(u v)(u uv v x 1) 0

v (x x 1) (x 1)u

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9

* 3 2 3 2u v 2x 1 3x 2 8x 15x 6x 1 0

2x 1

(x 1)(8x 7x 1) 0 1x

8

.

* 2 2 2 2u 3

u uv v x 1 0 (v ) (2x 1) x 1 02 4

2 2u4(v ) 12x 8x 7 0

2

2 2 2u4(v ) 4x 2(2x 1) 5 0

2 m.

V ghi m: 1

x 1; x8

.

( )f x " "

.

9: Gi 2 2 237x 13x 8 2x . x(1 3x 3x ) .

. Tuy nhiên . 2x .

32 3 2

7 13 8 1 32 3

x xx x x . (*)

1

tx .

33 2 28t 13t 7t 2 t 3t 3 .

3 2 23(2t 1) (t t 1) 2 2(2t 1) t t 1 .

t 23u 2t 1, v 2(2t 1) t t 1 , ta có h

3 23 3

3 2

u t t 1 2vu v 2v 2u

v t t 1 2u

2 2(u v)(u uv v 2) 0

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10

3 2u v 2t 1 t 3t 3 3 28t 13t 3t 2 0

2(t 1)(8t 5t 2) 0 2

t 1t 1

5 89t8t 5t 2 0

16

.

Th l i ta th y ba nghi m này th

V m: 16

x 1; x5 89

.

Tuy n

c

( )f x t t .

t

t x

. .

10: 2 22 2 1 (4 1) 1x x x x .

. 2 2 21 1 1(*)x t x t .

2 22( 1) 2 1 (4 1) 2 (4 1) 2 1 0t x x t t x t x . (**)

Xem (**

2 2

1

2

(4 1) 8(2 1) (4 3)

4 1 4 3 11

4 2(*)

4 1 4 32 1

4

x x x

x xt

x xt x

1t do (*). 2t t

v

2

2 2

2

2 1 12 1, 1 2 1

1 (2 1)

1 4.

33 4 0

xt x x x

x x

xx

x x

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11

t .

x

x - 1). .

1: 2 23 5 6 2 3x x x x x .

.

2: 2 22 6 7 5 3 5x x x x .

2 3 5t x x ; 0t .

PT 22 5 3 0t t . 3t . 2 3 5 3 1 4x x x x .

t

t .

ủ

3: 2 26 14 98 35 6x x x x

2 2 26 35 98 6 14 6 14 .t x x x t t t x

K

2

2

6 14

6 14

x x t

t t x

.

.

t ,x t .

trên.

. .

: Gi 3 38x 4x 1 6x 1 .

.

2 298 35 6 6 14t x x x x

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12

5 7x cos ;x cos ;x cos

9 9 9

.

: 3 31 3 3 1x x .

2 4 8

2cos ;2cos ;2cos .3 3 3

: 2 3

2 4 , 12

xx x x

.

3 17

4x

7: 2 4 2 2 2x x x .

5 17

2x

.

: 24 3 1 5 13x x x .

15 97 11 73

;8 8

x

.

: 33 2 2 32 10 17 8 2 5x x x x x x

33 2 2 21 4 2 7.

4

xx x x x x

232 32 2 15 20x x x . ( .

1 9 221

;2 16

x

.

2 210 6 2(2 1) 2 4x x x x x

: 17 97 17 97

;12 12

x x

.

2 22 12 6 2 2 4x x x x

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13

-8;-2; 0; 6}

G

22 4 3 5

2 2 52

x xx x

.

S= { 5 1 3 5

;2 4

}.

32 22 6 5 3 3 2x x x x .

3 5 3 5

;2 2

}.

.

2 2011 2011 2011 2011x x

2011 2011 2011

2011 2011

2011

y x

z x

t x

2

2

2

2

2011

2011

2011

2011

x y

y z

z t

t x

Minhduy_k16_THD@yahoo. com.