2 radicales

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



! 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:



"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

2 radicales

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