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2012二试 (1)

发布时间:2013-12-22 14:41:48  

2012().(40)

,ABCD,A,AB

ADBD,O2CB,CDBD,

:∠APO1=∠CPO2

.

.(40)

x1,x2,···,xnx1+x2+···+xn=n.

x1x2···x1nx+···+1

2BDACEO1:E,O1PEAB,CDP.

.(

40

)

,

ABCD,

,

A

,AB

BD

AC

E,

O1

AB,

AD

BD

O2

CB,CD

BD

,

E

O1

PE

CDP.

:∠APO1=∠CPO2

.

,

O1,O2

AC

,

O1

O2

BD

E,

,PE⊥

,

AC,PE=EC.

AB=AD=AE=a,

√a

O1E==(

2+1√

(

AC=

2?1)a,√

2+1)O1E=a,

O1E=EC=PE=

2?1

a=2+1∠APE=

(

2+1)EO2=(2?1)2a=PE2,

,∠APO2=90?.

Rt△APE~Rt△PO2E.

∠PO2E.

∠APO1+∠O1PO2=∠O1PO2+∠CPO2=90?,.(

,∠APO1=∠CPO2.

40

)

x1,x2,···,xnx1+x2+···+xn=n.

x2

+···+

1

:

x1x2···xn

1

1

f(x1,x2,···,xn)??0.

x1

+.

xn

?n+3?3,

n=1n=2

,

n=k

,

.

n=k+1

x1

,

k+1

k+1,

x1,x2,···,xk+1,k+1

x2,

,

f(t,x3,x4,···,xk+1)??0.

t=x1+x2?1.

k+1

k

k

t,x3,x4,···,xk+1

1,t,x3,x4,···,xk+1,

f(1,t,x3,x4,···,xk+1)=f(t,x3,x4,···,xk+1)??0.

2

,f(x1,x2,···,xk+1)??f(1,t,x3,x4,···,xk+1),

(x1?1)(1?x2)

1

x4

+1

+···+

1

.

x3xk+1

x1=1,x2→0,x3+x4+···+xk+1→k.

,

x3+x4+···+xk+1

,

1

x4

+···+

1

x3+x4+···+xk+11

xk+1

??

(k?1)2

x3

+

?(k+1)+3??0.

??1

,f(x1,x2,···,xk+1)??f(1,t,x3,x4,···,xk+1)??0.

.

,

,

.(

50,

)

7

.

:

4

,

.

7

A1,A2,···,A7.

..

,

,

,

,

:C37

4

.

.

6

(1)6

,

2

Ai

xi

,5?xi

,

Ai

xi(5?xi)??

5

2i=1

6

xi(5?xi).

6×6

xi(5?xi)??

2i=1

(2)7

xi(5?xi)??20?18=2.4

.

△A1A2A3,

,

(1)63

,

,

2

.

A1,

2

,

△A1A2A3,

,6

3

.

9

,

7

2

Aj(1??

j??7),

Aj,

2

,

2

,

2

,

4

.

,

(3)

,

4

.

4

(

,

3

),(),

().

n,np?1?1(n+.(50)

.p(p??5)[1,p?2]

1)p?1?1.p2?.

p?1S={1,2,···,p?1},A={n|n∈S,np?1≡1(modp2)}.

.,1∈A,

p=2k+1,k??2,k?12

(2,3),(4,5),···,(2k?2,2k?1).

?i(1??i??k?1,i∈N),2i∈A,2i+1∈A,

n=,1??i??k?1(2i,2i+1)|A|??p2i?.1,|A|??p?1∈A.A,

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