[1] O 2 A (6,0), B(3,3) , AB 2:1 P, 1:2 Q 3 O, P, Q C (1) P ( , ) ,
Q ( , ) (2) C OP , OP , y = x + , PQ , PQ , y x =?
2 C , C
(x ? )(2y ++ )2
=
(3) C x 2 , O R , R OA
:1
[2]
( ) 3x y z ++=, 352222x y z ++=, 4911116222x y z
+
+= x , y , z ,
x y z
2x X =, 2y Y =, 2z Z = , x y z X Y Z ( ) , X , Y , Z
XYZ = , 352X Y Z ++=
, XY YZ ZX ++=
,
t 3 ()()()t X t Y t Z ???
()()()t X t Y t Z ???32()()t X Y Z t XY YZ ZX t XYZ =?+++++? 3
t =?
()(12
t t =?? )(t ? ) , X Y Z , 12
X =, Y = , Z = ,
log x X =, log y Y =, log z Z =
x = , y = , z =
a ,
x ()x f , 323()3x x a x a =?+f ()y x =f , x = a , x =
a
, 2 ( , )a
, (
, )
a
y = 2x ? a
x
C C l
y = a
x
, l m
y =
x C
y =? 2x + a
x
D D l S , S =
C m x , 0a
C m
T S T = a
=
, ,
S =
(1) {}n p
13p =, 1113
n n p p +=+ (1,2,3,)n =!
{}n p , n ,
()113n n p p +?
=?
(1,2,3,)n =!
, {}n p ,
2
1
n n p ?=
+
?
, n
1
n
k k p =∑(
)
1
1n
n =
?
+
(2) {}n a , 3 13a =, 23a =, 33a = , n
1
32
n n n n a a a a ++++=
, {}n b , {}n c , n , 21n n b a ?=,
2n n c a = {}n b , {}n c ,
12
43
a a a a +== , 53a =, 6a =
, 73a =
, 12343b b b b ==== ,
3n b = (1,2,3,)n =!
, 13b = , n ,
1n n b b +=
, 1n = , , n k = , 1n k =+ , 1
[ ] 1n = , 13b =, 23b =
[ ] n k = , ,
1k k b b +=
1n k =+ , n 2k , 21k ?
21
k
k b ++=
, 11
k k c ++=
, 2k b +
2k k k
b +=
, , 21k k b b ++= , 1n k =+
[ ], [ ] , n , , {}n b 3n b = , n 21n ?
1113
n n c c +=+ (1,2,3,)n =!
, 1c = , {}n c , (1)
{}n p
OA 5=, OC 4=, AOC θ∠= OABC , OA 3:2 D , A BD OC E , 0θπ
, OA a ="""#"#, OC c ="""## , t OE tc ="""##
(1) t cos θ
AE tc a =?"""##"#, DB c =+"""###, a c ?="## cos θ
, AE DB ?="""#"""#
()()
cos 1cos t θθ+=
+
(2) E OC θ , OC O, C , cos
r θ= E OC , 0 t 1 11r ?<< ,
cos θ r (r + ) ,
0 t 1
0 ( )1r + (r + )
r , θ ,
π
θπ
(3) 1cos 8θ=? AE BD F , BEF
, t =, OF =
"""#
, F AE 1: ,
OABC , BEF