alg aa
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8/2/2019 alg aa
1/4
(....)
2012 _3.1()
: 1 4
: :
: 1 2012
A.1. 34.
A.2. 125.
.3. . . .
. .
.1. f
4(x 1) 0+ , x IR .
4(x 2) 0 x IR
x 1 0+ x 2 0 , x 1 x 2 f { }A IR 1, 2=
.2. { }x A IR 1, 2 = f
2 22 2
4 4 (x 1) (x 2)(x 1) (x 2)f (x)
x 1 x 2 x 1 x 2
+ +
= = =
+ +
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8/2/2019 alg aa
2/4
(....)
2012 _3.1()
: 2 4
2 2 2 2
(x 1) (x 2) (x 1) (x 2) x 1 (x 2) x 1 x 2 3x 1 x 2 x 1 x 2
+ +
= = = + = + + =+ +
{ }x A IR 1, 2 = : f(x) = 3. f(2012) = 3.
.3. 18 3x f ( 2012) :
18 3x f (2012) 3(6 x) 3 3 (6 x) 3
1 1 x 6 1 x 1 66 x x 6 1 1 6 + +
x [5, 7] .
.1.1. :
x + 1 = 2
|| . x || . x + x = 2
1
(|| + 1).
x = ||2
1
x = || + 1 = ||
2 1 = (|| 1) (|| + 1).
IR 0 1 1 0 + > .
IR = || + 1 0,
IR , x,
( )( )( )
( ) ( )( )
2 1 x 1 1
1 x 1 x 1 1 1
+ +
+ = = =
+ +
: x 1= , IR .
.1.2. 3, 2, :
d(x,3) 2 x 3 2 1 3 2 4 2
4 4 2 2 62 2 2 4 + +
6 6 6
[ 6, 2] [2, 6]
2 2 2
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8/2/2019 alg aa
3/4
(....)
2012 _3.1()
: 3 4
2.
2
1: y ( 4)x 1 = + + , IR
2
2: y ( 4 3)x 2 = + + , IR
1 1 = 1 = 2
4,
1 1 xx, 2 2 = 2 =
2+ 4 3 2
2 xx.
1 xx :90 < 1 < 180 1 ,
1 = 1 < 0, 1 < 0 2
4 < 0 ( 2, 2)
- 4
- +
0 - +2
+
-2
0
2
2 xx :0 < 2 < 90, 2
2 = 2 > 0,
2 > 0 2
+ 4 3 > 0 (1, 3)
- + - 3 4
- +
0 -2
+
-1
0
3
-
1 xx 2
xx :
1
2
0 ( 2, 2)
(1, 2)
0 (1,3)
<
>
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8/2/2019 alg aa
4/4
(....)
2012 _3.1()
: 4 4
.1. A ( ) , *
:
= 1 + ( 1) , * , = 7 :7 = 1 + (7 1) = 1 + 6 7 = 11,
1 + 6 = 11 1 + 6.
(2) = 11 1 = 12 11 = 1, 4 = 1 + 3 = 1 + 3(2) = 5, f(x) = 1x
2+ 4x + 1, ,
f(x) = x2
5x + 1.
.2. K f(x) = 0 x2
5x + 1 = 0 x1, x2 x
2 5x + 1 = 0 Vieta:
1 2
5S x x 5
1
= + = = =
1 2P x x 1
= = =
.
:
2 2
1 2 2 1 1 2 1 2x x x x x x (x x ) 5 = + = + =
2 2 2 2 2 2
1 2 1 2 1 2 1 2 1 2 1 2
2 1 1 2 1 2 1 2 1 2
x x x x x x x x 2x x 2x xB
x x x x x x x x x x
+ + + = + = + = =
2 2
1 2 1 2
1 2
(x x ) 2x x 5 1B 23
x x 1
+ = = =
331 2 1 2
400(x x ) 2012x x 12 400 4 2012 1 12 = + + = +
32000 2012 12 0 = + =
.3. : 2x B 2 x A + = :
2 2x 23 2 x 5 0 x 25 x 5 0 + = + =
|| + || = 0 = 0 = 0.
2 2x 25 x 5 0 x 25 0 + = = x 5 = 0
x = 5.
