7/18/2019 2 RADICALES
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RADICALES EN R
1. mnn m bb = ; b ∈ R+
2. nnn baba .. = ; a, b ∈ R+
3.n
nn
ba
ba = ; a, b ∈ R+
Ejm (1)
5 25.5 5.225 10
744 7355 3
333
0;;22
==
>== x x x
Ejm (2)
0;3.8121
.884444
3333
>==
==
aaaa
x x x
Ejm (3)
0;381
.
81
;23232
34
4
4 124 16
4
1216
4
5
5 20
5
20
>==
==
y y x y x y x
x x x
4. nmm n aa .=
5. nm nm n baba . .
=Ejm (4)0;;5 243 4155.33 5 >=== y y y x x
Ejm (5)
( ) 40 6162.4.5 232.425 4 32
12 44.3 43 4
...).(
.
cbacbacba
bababa
==
==
CASO PARTICULAR 15 17 6 8
71 x + x +
140 714.5.7 717 5 4 323 x x x x x ==
8 11 2223
x + x +40 232.4.5 235 4 32 x x x x x ==
RECORDAR Sea: a > 0
( ) ( ) −++
=±+±+=
)(
)(1...11
3...
a
aaaaa
aaa
Ejm.:
6.5
)(5...303030
4.3
)(4...121212
3...333
−=−−−
+=+++
=
PROBLEMAS PROPUESTOS
1. Obtener el val r !e:R " a aa aa a 351 27.9.3 −−−
a# $ b# 27 %# 81!# 243 e# 72$
2. Re!&%'r:
( "(
−
−−−
b
aa
b
bb
abb
aaa
1111
..
a# 1 b# )1 %# b a
!# a b e# ab
3. *al%&le & te! el val r !e:
radicalesn
n
5
5 5 5 5 45
5...−
−
a# 3125 b# 3120 %# 625!# 25 e# 5
4. S': x x " 2; x > 0
*al%&lar el val r !e: " x
x + x x
4 + x x
16
a# 1$ b# 20 %# 21!# 22 e# 24
5. S'm-l' '%ar:ab
baab
ababba
abbaabba−
++
++.
...
22
7/18/2019 2 RADICALES
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! n!e: a, b ∈ / ∧ b > aa# a b b# a %# b!# b a e# ab
6. a ' &'ente ex-re ' n:
( " nn
n
521
55
25−
−
E e &'valente a:a# 1 b# 5 %# 5!# 5 5 e# 25
7. a ' &'ente ex-re ' n:
"60123
3 4 5
3117
3117
a# 3 7 b# 4 11 %# 5 3
!# 1 e# 3
8. E e%t&ar:
"520
346
9.9999
a# 1 b# 3 %# $!# 3 3 e# 9 9
$. E e%t&ar:
/ "3 4 42
3 443
x x x
x x x
a# x b# x %# x!# x 4 e# x 5
10. *al%&lar el ex- nente 'nal !e x9 en:3 3 3 3 3 x x x x x
a#243
242b#
243121
%#243118
!#243241
e#243
1
11. Sab'en! &e:x " ...7575
" ...5757
%al%&le & te! el val r !e x 9 a# 5 b# 7 %# 35!# 2 e# 12
12. S'm-l' '%ar:
5 372
325 223
.
.
baba
bababa −
a# ab b# 5 ab %# ab!# 10 ab e# 1
13. E e%t&ar:E " ( )16
16 118 1111 55.55.5a# 20 b# 50 %# 250!# 300 e# 625
14. E e%t&ar:/ " ab 3 112 −−− abba
a# a b# b %# ab!# ab e# a
15. *al%&lar:
" ( ) 16
3 3
3 33
a# 1 b# 3 %# $
!# 81 e# 27
16. S'm-l' '%ar:17. Re!&%'r:
"n n
n nnn nn
16
2323
+
+++ −−
a# 2 3 b# 5 6 %# 6 5!# 3 2 e# 4 3
18. Sab'en! &e:
( " 4
1
8
1
32
4
642
<ar % m re -&e ta el val r !e:2
K
a# 2 4 b# 2 3 %# 22
!# 2 e# 1
1$. *al%&lar =9 ':
= "5
3
...90909022
...56565657
++++
−−−+
a# 1 b# 2 %# 4!# 8 e# 1 2
20. S' m + n " mn m, n ∈ /*al%&lar:
E "nm
m nn m
2222
+
+
a# 1 2 b# 1 4 %# 2!# 4 e# 1 8
TAREA
1. Re!&%'r:
7/18/2019 2 RADICALES
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"ba
ba
a# 1 b# 4 b %# b
!# 4 a e# ab
2. E e%t&ar:
"3 4 42
3 443
x x x
x x x
a# x b# x 2 %# x3
!# x 4 e# x 5
3. Re!&%'r:R " 5 64 53 43 ... aaaa
a# a b# a %# 3 a
!# 4 a e# 5 a
4. *al%&lar:? " ( ) 3/1
412 2739 a aa a −−
a# 1 b# 3 %# $!# 3 3 e# 3 9
5. &e !e e e%t&ar:
"( )( )
( )( ) 11
331
21
6
−−− x
x
@n!' &e el ex- nente 'nal !e x9 a# 1 b# 1 2 %# 1 4!# 4 3 e# 3 4
6. Aallar el ex- nente 'nal !e x9 en: x x x x .3
a# 1 2 b# 5 4 %# 1 4!# 3 4 e# 2 3
7. Aalle & te! el val r !e:
y x
x y
y x
y x
2
343
3
. ÷
a# y
xb#
x y
%# xy
1
!# 1 e# x1
8. *al%&lar el val r !e:
...424242274 +++++
a# 5 b# 7 %# 6!# 4 e# 10
$. *al%&lar el val r !e:
R "( ) ( )( ) ( )3
21
41
21
41
2
1 −
a# 1 b# 2 %# 4!# 8 e# 1 2
10. Aallar el val r !e:
E "nm nm
nm nnm m
− −
−− +3
9.69
< n!e: m, n ∈ + ∧ m > na# 5 b# 4 %# 3!# 2 e# 1
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