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200903


2009 3-

1.2009 (19x?31)(13x?17)?(13x?17)(11x?23)(ax+b)(8x+c) abc a+b+c= A?12 B?32 C38 D72 A 2.2009 [(17x2?3x+4)?(ax2+bx+c)](5x+6)(2x+1) 0 a?b?c= A3 B23 C25 D29 D 3.2009 ( ) A2m + 3n=5mn C ( x 2 ) 3 = x 6 A 4.2009 ax ? ax ? 2a
2

B a a = a
6 2

4

D a ? a = a
2

3



A. a ( x ? 2)( x + 1) C. a ( x ? 1) 2 A

B. a ( x + 2)( x ? 1) D. (ax ? 2)( ax + 1)

5.2009 x3 ? 2 x 2 y + xy 2 A. x ( x + y )( x ? y ) B. x x 2 ? 2 xy + y 2

(

)

C x( x + y)

2

D x( x ? y)

2

D 6. 2009 A a + a = a
2 3 5



B a a = a
6 2

3

C a 2

( )

3

= a6

D 2a 3a = 6a

. C

7. (2009 ) a b a b 2009 ) a a b A (a + b) 2 = a 2 + 2ab + b 2 B (a ? b) = a ? 2ab + b
2 2 2

a b b b

2 2 C a ? b = ( a + b)( a ? b)

D ( a + 2b)( a ? b) = a 2 + ab ? 2b 2

C 8.2009 ( ?3 x 2 ) 2 x 3 A ? 6x
5

B ? 3x

5

C 2x C a 2

5

D 6x

5

9. 2009 A a + a = a
2 3 5

B a a = a
6 2

3

( )


3

= a6

D 2a 3a = 6a

. C 102009 A a 2 a 3 = a 4 C a 2 + a 3 = a 5 B 112009 A a 2 a 3 = a 4 C a 2 + a 3 = a 5 B 12.2009(-3) . A.9 B.-9 C.6 D.-6 A 132009
2

B (?a 4 ) = a 4 D (a 2 )3 = a 5



B (?a 4 ) = a 4 D (a 2 )3 = a 5

.

A.a a =a B. Ca =a C. a a =a B 142009 A 2a + b = 2ab B ( ?ab) = a b
2 2 2
2

2

3

6

4

4

2

3

5

D.(a ) =a

2 3

5


2 2

C a a = 2a

D a a = 2
4 2

B 152009 A - (- 3) = 3 B 4 = 2
3


3

C (3 x ) = 9 x

D 2

- 1

=

1 2

C 16(2009 )1 ( a 3 ) 2 A a
5


9

B a

6

C a

8

D a

B 17(2009 )2 A a + a = a
3 3 6


6 2 4

B 2( a + b) = 2a + b C ( ab) ?2 = ab ?2 D a a = a

D 3 2 182009 a a 5 -1 2 Aa Ba Ca Da C 192009 ڧ A a a = a
6 3 2



B (a 3 ) 2 = a 5 D 6 3 =

C 2 2 + 3 3 = 5 5

2

D ȧ ȦȦ D 202009 A a + a = a
2

B a a = a
2

2

2 2 C (2a ) = 4a

D (a 3 ) 2 = a 5

C a + a = 2a A

a.a 2 = a1+ 2 = a 3 B a ( a 3 ) = a 23 = a 6 D
2

21. 2009 ާ A a = a a
2 3 6



B ( 2a 3a ) = 6a )(
2 3 5

C a

( )

2 3

= a6

D a a = a
6 2
2

3

a a = a A ( 2a 3a ) = 6a B )( a 2

( )

3

= a 6 C C

C 222009 3 x + 9 x 3 x + 4 x ? 1
2 2

A ?5 x ? 1

B 5 x + 1

C ?13 x ? 1
2

D 13 x + 1
2

3 x + 4 x ? 1 - 3 x + 9 x = ?5 x ? 1 A A 23. 2009  D A a a = a
2 3 6

B a a = a
8 4

2

C a + a = a
3 2

5

D 2a 2

(

)

3

= 8a 6

2a 2 D

(

)

3

= 8a 6 D

242009 ( a 2 )3 A a
5


2

B a

6

C a

8

D 3a

B 252009 3a ? a ? 2 = 0 5 + 2a ? 6a =
2 2



1 262009

A2 a + a =3 a

B2 a ? a =1

C2 a a =3 a

2

D2 a a = a

A 272009 糧 糧 A a a = a
3 2 6

B ( ? 3.14) = 1
0

?1? C ? ? = ?2 ? 2?

?1

D 9 = 3

B 282009 A 3a + 2a = a
5 2


3 6

B a ? a = a

C ( a + b)( a ? b) = a 2 ? b 2

( a + b) 2 = a 2 + b 2

C 292009 a + b + c . (a ? b) 2 ab + bc + ca a b + b c + c a (
2 2 2

) D

A B C A 302009 5 A 2a + b = 2ab B ( ?ab) 2 = a 2b 2


2 2 2

C a a = 2a

D a a = 2
4 2

B 312009 11 A ( a 3 ) 2 = a 6 B a 2 ? a = a 2 C a + a = a 2 D a 6 a 3 = a 2

A 322009 ( Aa-b2=a2-b2

)? D 3 3 -2 2 =1 ?

Ba2a3=a5 ? C 2a+3b=5ab

B 332009 a2a3

Aa5 Ba6 Ca8 A 342009 A ( x ) = x
3 3
4

Da9


4 24

6

B a = a a
6 2 2 2 6 3

C (?bc ) ( ?bc ) = b c C

D x x = x

2

352009 2 x ? 8 x + 8
2


2

A ( 2 x ? 4 )

2

B 2 ( x ? 4 )

2

C 2 ( x ? 2 )

2

D 2 ( x + 2 )

C 36(2009 )ާ (2009 ) 2 4 6 3 2 6 Ax x x B2x +3y5xy C(x ) x C

Dx x x

6

3

2

372009 2009 2 x = 3,4 y = 5, 2 x -2y

A

3 5

B-2C

3 5 6 D 5 5

A 382009 ?2a + ( 2a ? 1)



A ?4a ? 1 B 4a ? 1 C 1 D ?1 D 392009 A ?2(a ? b) = ?2a ? b B ?2(a ? b) = ?2a + b C ?2(a ? b) = ?2a ? 2b D ?2(a ? b) = ?2a + 2b D 402009 A a 2 ? a 4 = a 6 A 412009 8. 2 x ? 8 x + 8
2

C y 2 y 3 = y D 3ab ? 3a b = 0
2 2

B ( x 2 )5 = x 7



A ( 2 x ? 4 )

2

B 2 ( x ? 4 )

2

C 2 ( x ? 2 )

2

D 2 ( x + 2 )

2

C 42 11. 422009 11. 3 2 6 2 3 5 A a ? a = a B ( a ) = a C a a = a
8 2 4



D (ab ) = a b
2 2

2 4

D 432009 ab A a b
2 2

( )

3 2

=
2 6

D ab
6

B a b

2 3

C a b

C 442009 A (m ? n) 2 = m 2 ? n 2
2 2 4 C m ? n = (mn)


?2

B m

=

1 ( m 0) m2

D ( m 2 ) 4 = m 6

B 452009 x ? 3 y = ?3 5 ? x + 3 y A0 B2 C5 D8 D 462009 A 2 6 2 2 = 2 3 B 47 472009 ? ? 3a 2b3 ( B (2 3 ) 2 = 2 6 C 2 = 0
0



D 2 ?1 = ?2

(

)

4

) D. ? 81a 8b12

. 81a8b12 B. 12a 6b7 C. ? 12a 6b 7 D. 482009 3 3 6 8 2 4 A.x+x=2x B. 2xx=1 C.(x ) =x D. x x =x , A . 492009 2 x x
3 2



A x

B 2x

C 2x

5

D 2x

6

B 502009 A. C.

B. D.

( x ? y) 2 = x 2 ? y 2 a6 a3 = a2

x3 ? x2 = x5 (x 2 )3 = x 5

B. 512009 A a ? a = a
2 3 6


2 2 4 3

B a + a = a D a a = a

C (? a 2 )3 = ? a 6

C 522009 C A a + a = a
2

B a a = a
2

2

2 2 C (2a ) = 4a

D (a 3 ) 2 = a 5

532009 A a a = a
2 2

B B ab 2

( )

2

= a 2b 4

a C a = a
2 4

8

D 5ab ? 5b = a D

542009 ڧ A a a = a
6 3 2

B (a 3 ) 2 = a 5 D 6 3 =

C 2 2 + 3 3 = 5 5

2


55(2009 ) ( x ?1 ) 2 x3 A x
5

B x

4

C x

D

1 x

C 562009 A x + x = x
3 4 2 8 C ( x ) = x 4

B x x = x
2 5

10

D x 2 + x 2 = x 4 ( x 0)

C 572009 2 2 2 3 5 3 A3a a 3 Ba a Ca A6a9 D2a22a2 CA 2 a2B a6C D 2 4 a2 582009 x + x = 2 x ( x 2 )3 = x 6 3 2 ? 1 = 5 ? ?5 + 3 = 8 1 2
2 3 5

0

1 =1 2

A1 B2 C3 D4 A

3 2 592009 ( a )


8

A a

6

B a

9

C a

5

D a

A 602009 0 < x < 1 x A

1 < x < x2 x

B x <

1 < x2 x

1 2 x x 1 1 2 2 C x < x < D < x < x x x

C 612009 A 2a + a = 2a
2

C (a 2 )3 = a 5 D a a = a
3 2

B ( ?a ) 2 = ? a 2

D 622009 3 A.2x+x=x 2 2 C.(x-2) =x -4 632009 A a a = a
3 4 12

B.(3x) =6x 2 D.x x=x
3

2

2

B a a = a
6 3

2

C 2a ? 3a = ? a

D ( a ? 2) 2 = a 2 ? 4

642009 A (m ? n) = m ? n
2 2 2


?2

B m

=

1 ( m 0) m2

C m 2 ? n 2 = (mn) 4 B

D ( m 2 ) 4 = m 6

652009 x ? 3 y = ?3 5 ? x + 3 y A0 B2 C5 D8 D 3.2009
6 2 3 A 2 2 = 2



B (2 3 ) 2 = 2 6

C 2 = 0
0

D 2 ?1 = ?2

B 66(2009 ) (2009 ) A 6a ? 5a = 1 D B (a ) = a
2 3 5

C a 6 a 3 = a 2 D a ? a = a
2 3 5

67(2009 ) ( ) A 4m ? m = 3 B ?(m ? n) = m + n
C m 2 = m6 3 C 68(2009 ) A a a = a
2 3 6

D m 2 m 2 = m

C 16 = 4 D | ?6 |= 6

?1? B ? ? = ?2 ?2?

?1

,, D 69(2009 ) A x + x = x
2 3 2 5


6

B ( x ) = x
2 3

C ( x ? 2) = x ? 4
2

D x x

?1

=0

B 7009



A ?22 + ( ? 3.14)0 = 5

B ? ? = 8 ? 2?

? 3?

?3

27

2 x D ab 2 + a 2 b = a3b3 C x 3 = x 5 C

7109 A 3 x x = 2 x
2

C x x = x
3 4 12

B ( x 2 ) 3 = x 5

D 2 x + 3 x = 5 x
2 2

2

D 722009 3 A a 2 a 3 = a 4 C a 2 + a 3 = a 5

B (?a 4 ) = a 4 D (a 2 )3 = a 5

B 732009 2 A x = 2 x x
2 2 4



B ( x 2 )3 = x8 D x = x x
4 2 8

C x x = x
4 2

2

742009 A x x = x
6 2 3 2 3



B (?3 x) 2 = 6 x 2 D ( x 3 ) 2 x = x 7

C 3 x ? 2 x = x

D
n 64a 8 74 752009 a a a a (

) D n
a

A na

B n + a

C a

n

C 762009 ۧ( A ?2) 2 = ?22 ( B 10 = 10 10
5 8 40

) D

C2 x + 3 y = 5 xy

x2 + y = x+ y x

A

77 (2009 ) A.a2a=3a
2 3 2 6

B. 3a2a=a D.6a 2a =3a
2 2 2

C. a ? a =a B 78. (2009 ) A.a2a=3a 2 C. a ? a =a B
2 3 6

B. 3a2a=a D.6a 2 2a 2 =3a 2

792009 2 a A a
6

( )

3 2


5

D a
8

B a

9

C a

A 802009 A a a = a
6 2 3



B

( ?2 )

?1

=2

C

( ?3 x x )2
2

3

= ?6 x 6

D ( ? 3) = 1
0

D 812009 1 m n m > n 2ʦ A m n n

m?n 2

B m ? n

C

m 2

D

n 2

1

n 2

A 822009
0 A. ? 2 2 + ( ? 3.14 5

B.
2

3 2

?3

27 8
3 3

C. x ? x = x
2 3

5

D. ab + a b = a b
2



n 64a 8 74 832009 a a a a (

) D n
a

A na

B n + a

C a

n

C 842009 ۧ( A ?2) 2 = ?22 ( B 10 = 10 10
5 8 40

) D

C2 x + 3 y = 5 xy

x2 + y = x+ y x

A 852009 A a + a = 2a
3 3 3

D 2a a = 2a
3 2

B a = a a
2 3

5

C ( ?a 3 ) 2 = a 9

C 86 ? ? 3a 2b3 B 12a 6b7 81a8b12 D 87( A ( x 2 )3 = x 5 C (? x )9 ( ? x)3 = x 6
2

(

)

4

D ? 81a 8b12

C ? 12a 6b 7

) B 3 x + 4 x = 7 x
2 4

D ? x( x 2 ? x + 1) = ? x 3 ? x 2 ? x

C 88( A x 2 ? y 2 = ( x + y )( x ? y ) C x 2 + xy = x( x + y ) D
892009 A a + a = 2 a
3 3 3

) B x 2 + 6 x + 9 = ( x + 3) 2 D x 2 + y 2 = ( x + y ) 2


3 2 9

B a = a a
2 3

5

C ( ?a ) = a

D 2 a a = 2a
3 2

C

90 ? ? 3a 2b3 81a8b12 B 12a 6b7 D 91( A ( x ) = x
2 3
9

(

)

4

D ? 81a 8b12

C ? 12a 6b 7

) B 3 x + 4 x = 7 x
2 2 4

5

C (? x ) ( ? x) = x
3

6

D ? x( x ? x + 1) = ? x ? x ? x
2 3 2

C 92( A x 2 ? y 2 = ( x + y )( x ? y )
2 C x + xy = x( x + y )

) B x 2 + 6 x + 9 = ( x + 3) 2 D x 2 + y 2 = ( x + y ) 2

D 932009 A 2 x x = 6 x 3
2 2 4 2 2



B 2 x ? 3 x = ?1 D 2 x + 3 x = 5 x
2 2 4

C 2 x 3 x =
2 2

2 2 x 3

A BD A 94(2009 ) A (a ? b)2 = a 2 ? b2 C (
1 ?1 ) =3 3

B-23 = 8 D a 6 a3 = a 2

C 95 2009 A 2 x x = 6 x 3
2 2 4 2 2



B 2 x ? 3 x = ?1 D 2 x + 3 x = 5 x
2 2 4

C 2 x 3 x =
2 2

2 2 x 3

A BD A

2009 2 m+n=3 2m + 4mn + 2n ? 6
2 2



12 6 A

3

0

1.2009 a=1.6109b=4103 a22b= (A) 2107 (B) 41014 (C) 3.2105 (D) 3.21014 D 22009 x + 3 x= x ( x + 3)
2

.

3.2009 m 0.4 n 2 . 0.4m + 2n 4.2009 ( ?3 x 2 ) 2 x 3 A ? 6x
5

B ? 3x

5

C 2x

5

D 6x

5

A 52009 ax ? ay = a ( x ? y ) 6. (2009 ) ? x 3 ? 2 x 2 ? x = _____________ 2009 ) -x(x+1)2 72009 ax ? ay = a ( x ? y ) 8. (2009 ) ? x 3 ? 2 x 2 ? x = _____________ 2009 ) -x(x+1)2 92009 5a ? 2a = 3a



1012009 n n 2n+2 112009 a2b-2ab2+b3=____________________. b(a-b)2B 13 122009 a 2 ? b 2 ? 2b ? 1 = B 132009 5a ? 2a = 3a 142009 n n 2n+2 152009 a2b-2ab2+b3=____________________. b(a-b)2B 13 162009 a 2 ? b 2 ? 2b ? 1 = B 17 a 2 ? b 2 ? 2b ? 1 = (a + b + 1)(a ? b ? 1)

18 4m 45 60 m 2( 3 ? 2) 192009 m - m = _______________ m( m - 1) 202009 m ? mn + mx ? nx =
2 2



(m ? n )(m + x )

212009 x + 3 x =
2



x ( x + 3) 22(2009 )8 3 x ? ? ?
3

? 1 2? x ? =________ ?(?2a 2 ) 4 =________ ? 9 ?

, ?

x5 3
3

23 (2009 )9 6a ? 54a =________; 6a (a + 3)(a ? 3) 24(2009 ) a ? ab ______________
3 2

a (a + b)(a ? b) 252009 x+3 -(x+3) ___________ (x+3)(x+2) 262009 2a ? 4a =
2
2



2a ( a ? 2) ---- 2a 272009 x3 ? xy 2 ___________ xx+yx-y 282009 x = 2

2 x 2 ? 3x + 3 2 _____________

292009 10 = 2 = 3 10 10
m n

3m + 2 n

= ____________

72 302009 y 3 y 312009 (3a ) 2 a 5 = 9 a
7

( )

2

y5 =

32.2009 x ? 4 = _____________
4

( x 2 + 2)( x +

2 )( x ? 2 )
2

332009 13 x + 3 x = x(x+3) 342009 5: x ? 4 =
2





(x+2)(x-2) 352009 12 x ? 2x =
2



x (1 ? 2 x )

362009 3 x m +5 y 2 x 3 y n n =
m





1 4

372009 x 45% ________ 0.55 x

382009 2a ? 8a = ____________
3

2a ( a + 2)(a ? 2) 392009 x = 3y = 1 (x + y )(x ? y ) + y
2



9 402009 a b a b
3 2

( )
2

2

a



412009 abcd ac bd ab? cd=acbdadbc ab=cd ? 12 ? pq=50 p q 1C2; 422009 2009 2 x = 3,4 y = 5, 2 x -2y

A

3 5

B-2C

3 5 6 D 5 5

A 432009 ( x + y ) 2 ? 3( x + y ) = ( x + y )( x + y ? 3 )
44 2009 x 120 __________







120 ? x ? 120 ? x ? 100% ? ? x x ? ?

452009 8 10 10 10 x y ա
x y 2 16 7 10 22

5680156.8

462009 14. a b a b
3 2

( )
2

2

a



472009 2.a b 472009 2. a+b 2009 11. x = 3y = 1 (x + y )(x ? y ) + y 2 9 482009 ax ? a =
2





.

ax+1x-1 492009 6 1 4 2 7 n (n ) (3) 6

(1)

(2)

3n+1 502009 7- 7- 7- 7- 5 ________ n ________

51(2009 ) A 9 = 3 B (a 2 ) 3 = a 6 C 3a ? 2a = 6a D 3?2 = ?6

B 52 x - 4x + 4 x =_________
3 2



x(x-2)2 532009 2 xy x+y+xy+x+y. x 2 ? y 2 + x ? y + x + y x ? y + 2x
2 2

542009 x = 2 x + 3
2 2

.

5 552009 x ? 2 x =
2

xx.

562009 2 x ? 8 =
2





2 x + 2 (x ? 2)
57(2009 ) x = 3y = 1 (x + y )(x ? y ) + y 2 9 582009 a22a__ aa2 592009 2 x ? 18 2x3x3
2





602009 2a ? 4a =
2

2a ( a ? 2)

61(2009 )10 xy 2 ? 9 x = x ( y + 3)( y ? 3)

62(2009 )9 m ? mn =
3 2



m( m + n)( m ? n) 63(2009 )11 a + b = 2 a ( a + 2 )( a ? 2 ) 642009 A x + x = x
3 4

3 ab = 1 ( a ? 2)(b ? 2) 2



B x x = x
2 5

10

C ( x 4 ) 2 = x8 C

D x 2 + x 2 = x 4 ( x 0)

65(2009 ) ( x ?1 ) 2 x3 A x
5



B x

4

C x

D

1 x

C 662009 x34x



x( x + 2)( x ? 2)

67.2009 m ? 2m = 1 2m ? 4m + 2007 _______________
2 2

2009 C 3 682009 x -4x= x(x+2)(x-2) 692009 x ? 9 =
2

.





(x+3)(x-3) 702009 ( x + 1) + 2 (1 ? x )
2

( x + 1) + 2 (1 ? x ) = x + 2 x + 1 + 2 ? 2 x = x + 3
2
2 2

C 712009 9a ? a =
3

2 x ? 12 x + 18 =
2



a (3 + a )(3 ? a )

2( x ? 3) 2
2

722009 ax ? a =

.

ax+1x-1 732009 6 1 4 2 7 n (n ) (3) 6

(1)

(2)

3n+1 74(2009 ) mn mn 2 ? (n ? 1) ( ) , 1
75(2009 ) 27 x + 18 x + 3 =
2





3(3 x + 1) 2
7609 H1N1 30% a /____________/

0.7a 70%a

7 a 10

7709 3a + 6ab + 3b =
2 2



3( a + b) 2 2009 12 a 2 ? b 2 ? 2b ? 1 = (a + b + 1)(a ? b ? 1) 78(2009 )mn m_______________________. m(n+1)(n-1) 79(2009 ) ab1ab=-2(a1)(b1)___________________. -4 80(2009 )mn m_______________________. m(n+1)(n-1) 81(2009 ) ab1ab=-2(a1)(b1)___________________. -4 822009 2 x ? 8 x =__________
3



2

2

2 x ( x + 2 )( x ? 2 ) 832009 3 __________ n __________ n

1

2

3

10 3n + 1 842009 n

1 2 3

3n + 2 852009 H1N1 30 a /___________/ 0.7a 70%a

7 a 10
3

862009 a ? 4a = a ( a + 2)( a ? 2) 872009 2 x ? 4 x + 2 =
2





2( x ? 1) 2 B 882009 x 3 ? 2 x 2 y + xy 2 = x ( x ? y ) 2

1 892009 ( ? 2 a ) ? ( a 3 ? 1) = 4
?



1 4 a + 2a 2
3 n +1

902009 2a b

? 3a

m? 2

b 2 2m + 3n =



13 91(2009 ) x 2 5 ______.



x?2 5
2

92.2009 2 x ? 4 x + 2 = 2( x ? 1) 2 932009 C.a+a=a2 Aa2a=3a B.a6a2=a4 B 942009 3x3-6x2+3x= D.(a2)3=a5



.

1.2009 x ? 5 x = 14 ( x ? 1)( 2 x ? 1) ? ( x + 1) + 1
2
2

( x ? 1)( 2 x ? 1) ? ( x + 1) + 1
2

= 2 x 2 ? x ? 2 x + 1 ? ( x 2 + 2 x + 1) + 1 = 2x ? x ? 2x + 1 ? x ? 2x ?1 +1
2 2

= x ? 5x + 1
2

x ? 5 x = 14
2

= ( x 2 ? 5 x) + 1 = 14 + 1 = 15 22009 1

1 1 2 2 3 3 = 1 ? 2 = 2 ? 3 = 3 ? 2 2 3 3 4 4

1 n 2 n n 1 n =n? n +1 n +1 2

n2 + n ? n n2 n n n =n? 8 n +1 n +1 n +1 n +1

32009 | ?2 | +2sin 30o ? (? 3)2 + (tan 45o ) ?1 2 + 1 ? 3 + 1 1

4 2009 (a + b) + ( a ? b)(2a + b) ? 3a
2

2



a = ?2 ? 3b = 3 ? 2
( a + b) + ( a ? b)(2a + b) ? 3a = a + 2ab + b + 2a ? ab ? b ? 3a
2 2 2 2 2 2 2

= ab
a = ?2 ? 3 b =

3 ? 2
2 2

= ( ?2 ? 3)( 3 ? 2) = ( ?2) ? ( 3) = 1 5(2009 ) x 2 (3 ? x ) + x ( x 2 ? 2 x ) + 1 x = 3 2 3 3 2 =3x -x +x -2x +1 2 =x +1 x= 3 =4

62009

1 (a + b)(a ? b) + (a + b) 2 ? 2a 2 a = 3b = ? 3
2 2 (a + b)( a ? b) + ( a + b) ? 2a

= a 2 ? b 2 + a 2 + 2ab + b 2 ? 2a 2 = 2ab 5
a = 3b = ?

1 ? 1? 2ab = 2 3 ? ? ? 3 ? 3?

= ?2 6
72009 x 2 + 2 xy , y 2 + 2 xy , x 2 ( x 2 + 2 xy ) + x 2 = 2 x 2 + 2 xy = 2 x ( x + y ); ( y 2 + 2 xy ) + x 2 = ( x + y ) 2 ; ( x 2 + 2 xy ) ? ( y 2 + 2 xy ) = x 2 ? y 2 = ( x + y )( x ? y );
2 2 2 2 ( y + 2 xy ) ? ( x + 2 xy ) = y ? x = ( y + x )( y ? x ).

82009 a b c

a+b b+c c+a 2 2 2

. a,b,c 2 ab

a+b . 2

5.2009 ( a ? 2)( a + 2) ? a ( a ? 2) a = ?1 2009 = a ? 4 ? a + 2a
2 2

= 2a ? 4 a = ?1
= 2 ( ?1) ? 4 92009 17 6 3( x ? 1) ? ( x ? 5) x = 2 = 3 x ? 3 ? x + 5 2 = 2 x + 2 4 x = 2 = 2 2 + 2 5 6 =6 ߧ 1 102009 x = 3 + 1 y =

3 ? 1 .

1 x 2 + 2 xy + y 2 3 2 x 2 ? y 2 3

1 ( x + y ) 2 ( 3 + 1 + 3 ? 1) 2 (2 3) 2 12 2 ( x + y )( x ? y ) [( 3 + 1) + ( 3 ? 1)][( 3 + 1) ? ( 3 ? 1)] 2 3 2 4 3 112009 (a + 2b)(a ? 2b) ?
1 b(a ? 8b) 2

(a + 2b)(a ? 2b) ?

1 1 1 b(a ? 8b) = a 2 ? 4b 2 ? ab + 4b 2 = a 2 ? ab 2 2 2

122009 20.

1 ? 1 ? ? ( x ? 2 ) x = 2 ?1 + ? 2 ? x ?1 ? x ?1
? 1 +

? ?

1 ? 1 ? ( x ? 2) ? 2 x ?1 ? x ?1

=

x ( x + 1)( x ? 1) ?x+2 x ?1 1

= x2 + 2
x= 13 17. 132009 17. ( x + y )( x ? y ) ? 2x + y ( x ? y) xy2xy x2y x3y2 341 142009 a2b2 2ab (1) a=3b=4 a2+b2+2ab (2) (1) a=3b=4 a2+b2+2ab= (a + b) 2 =49
(2) 2 2 a2b2 a2-b2=(a+b)(a-b) a22ab a22ab=a(a2b) 152009 a2b2 2ab (1) a=3b=4 a2+b2+2ab (2)

2 =

( 2)

2

+2 =4

x2 ? y2 ? 2 x + y x =3 y =2 x? y

(1) a=3b=4 a2+b2+2ab= (a + b) 2 =49
(2) 2 2 a2b2 a2-b2=(a+b)(a-b) a22ab a22ab=a(a2b) 162009 ( a ? 3 )( a + 3 ) ? a ( a ? 6) a =

5+

1 2


17 (2009 ) a =

2007 2008 b = ab 2008 2009

a=

2007 2009 (2008 ? 1) (2008 + 1) 20082 ? 12 = = 2008 2009 2008 2009 2008 2009 20082 b= 2008 2009 20082 ? 12 < 20082

a<b 182009

1 (a + b)(a ? b) + (a + b) 2 ? 2a 2 a = 3b = ? 3
(a + b)( a ? b) + ( a + b) 2 ? 2a 2

= a 2 ? b 2 + a 2 + 2ab + b 2 ? 2a 2
= 2ab 5
a = 3b = ?

1 ? 1? 2ab = 2 3 ? ? ? 3 ? 3?

= ?2 6
(2)(3+m)(3-m)+m(m-6)-7 m=

1 2

2=9m2+m26m-7=6m+2 m=

1 1 =6 +2=1 2 2
2

19(2009 ) n=123 n 6n

n -6n n ? 2 » n=7 n -6n=7>0 2 2 n -6n=n(n-6), n -6n0 202009

2

1 2 1 1 x + 2 x ? 1 x 2 + 4 x + 1 x 2 ? 2 x 2 2 2



1 2 1 x + 2 x ? 1 + x 2 + 4 x + 1 = x 2 + 6 x = x( x + 6) 2 2 1 2 1 2 2 x + 2 x ? 1 + x ? 2 x = x ? 1 = ( x + 1)( x ? 1) 2 2 1 2 1 2 2 x + 4 x + 1 + x ? 2 x = x + 2 x + 1 = ( x + 1) 2 2 2
5+ 1 2

212009 ( a ? 3 )( a + 3 ) ? a ( a ? 6) a = 22(2009 ) 9 + 20090 ? 2 cos 60 (2009 ) ,0 , 1 311 3 23(200915 ?3 ? ( ? 1) 0 ? ? ?

?1? ?2?

?1

242009 a+b=3ab=2 1a2b+ab2 2a2+b2 1 a 2 b + ab 2 = ab( a + b) = 2 3 = 6 3 2 (a + b) 2 = a 2 + 2ab + b 2 a 2 + b 2 = ( a + b) 2 ? 2ab = 3 2 ? 2 2 = 5 6 ?a + b = 3 ? ?ab = 2
a =2 ? 1 ? ?b1 = 1 ?a 2 = 1 2 ? ?b2 = 2

a = 2, b = 1 a 2 b + ab 2 = 4 + 2 = 6, a 2 + b 2 = 4 + 1 = 5 4 a = 1, b = 2 a 2 b + ab 2 = 2 + 4 = 6, a 2 + b 2 = 1 + 4 = 5 6

1 4 2 252009 ( x + 3) ? ( x ? 1)( x ? 2 )
2

= x 2 + 6 x + 9 ? x 2 ? 3 x + 2 = x + 6 x + 9 ? x + 3x ? 2
2 2

(

)

= 9x + 7


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