Συνοπτική Θεωρία Άλγεβρας ,Β Λυκείου
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Transcript of Συνοπτική Θεωρία Άλγεβρας ,Β Λυκείου
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. :
f x x 2.
2 2 x x x
f x x 2.
2 2 x x x
f x x .
x x x .
f x x .
x x x .
f x x .
2 [0 2], .
1. R
2. f
2x
1
2f
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16
3. f
2 2
x , Z
4. f 3
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x 0
2
3
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f x x .
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0 2 1f f . 3. f 2 x , Z
4. f x 1f 5. f 2 x , Z
6. f 2,
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2 2 , , . 8. f y.
9. f x
2
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g x x
f x x x.
1. R
2. 2
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3. 4. . 5.
x 0
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f x x 0 - 0
6. g
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f x x .
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1. 0R x / x
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2. .
3.
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5. f x
x , Z .
f x x .
[0 ], .
1. 0R x / x R x , 2. .
3. 0 , 4. f x
2
x , Z .
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x
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x
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x
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x
R : a :
x x ,
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0 x x ,
1 2
2x x ,
1 2
2x x ,
0
2x x ,
1 2 x x ,
1 2 x x ,
0 0 x x x ,
0 0
2x x x ,
.
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x ax
a R . x .
x :
1
1 1 0....a x a x a x a
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0a .
1 1 0, ,....., ,a a a a , .
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0P x , . .
x .
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() .
x
P() x=.
P()=0 .
P()=c c ( ).
(
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22
.
.
( ): (x) (x) (x) 0 (x) (x), : (x)=(x)(x)+(x), (x) (x) () , () , () ()
. : P(x) x- x=. =P() : P(x) x- P(x), P()=0. ( ):
1
1 1 0.... 0a x a x a x a
, .
0
0a .
.
.
:
P(x) x - x - P(x) x - P(x) P(x) x - x - P(x) P(x) x - P(x) P()=0 P(x): x -
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:P x x a P a .
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:P x ax Pa
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24
0 1xf x a , a , x R , .
0 1 0ag x log x, a , x , .
y=x .
x
aa y x log y
1 2
1 2
1 2
1 2
1 1
x x
x x
a a
a a x x
log log a x x
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25
0 1a x af x a , g x log x .
1 2x x
1 2
1 2
1 2
1 2
1 2 1 2
1 2 1 2
x x
x x
a a
a a
a a x x ,
a a x x ,
log x log x x x ,
log x log x x x ,
1a x af x a , g x log x .
1 2x x
1 2
1 2
1 2
1 2
1 2 1 2
1 2 1 2
x x
x x
a a
a a
a a x x ,
a a x x ,
log x log x x x ,
log x log x x x
1 1 0xalogx
a a alog a , log , log a x, a x
10 1 1 0 1 1 0log , log , lne , ln
1 2 1 2 alog log log
1 1 2 1 2
2
0
alog log log , ,
0 a alog log , , R
1 0
a alog log , ,
10log x log x
elog x ln x