ejercicio 211 del libro de Baldor

5
Ejercicio 211 del libro de Baldor . ( + ) = () + 6() (2) + 15() (2) + 20() (2) + 15() (2) + 6()(2) + (2) = + 6 (2) + 15 (4 ) + 20 (8 ) + 15 (16 ) + 6(32 ) + 64 = = + + + + + + . ( − " ) = (2# ) + 5(2# ) (−3$ ) + 10(2# ) (−3$ ) + 10(2# ) (−3$ ) + 5(2# )(−3$ ) + (−3$ ) = 32# %& + 5(16# )(−3$ ) + 10(8# )(9$ ) + 10(4# )(−27$ * ) + 5(2# )(81$ % )−243$ % = 32# %& + 80# (−3$ ) + 80# (9$ ) + 40# (−27$ * ) + 10# (81$ % )−243$ % = = + " + , " − + " + + " − " . (- +. ) = (/ ) + 6(/ ) (0 ) + 15(/ ) (0 ) + 20(/ ) (0 ) + 15(/ ) (0 ) + 6(/ )(0 ) + (0 ) = / % + 6(/ %& )(0 ) + 15(/ )(0 ) + 20(/ )(0 * ) + 15(/ )(0 % ) + 6(/ )(0 % ) + (0 %’ )= =- + - . + - + . + - . + - . + - . +. + 4. 4. 4. 4.- ( - . , ) , = (3) 3 + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (3) (−0 3 ) + (−0 3 ) 3 = (3) 3 + 7 (3) (−0 3 ) + 21(3) (−0 3 ) + 35(3) (−0 3 ) + 35(3) (−0 3 ) + 21(3) (−0 3 ) + 7(3) (−0 3 ) + (−0 3 ) 3 = R= R= R= R= 2187 2187 2187 2187 – 5103 5103 5103 5103 . , + 5103 + 5103 + 5103 + 5103. −2835 2835 2835 2835. + 945 + 945 + 945 + 945. + − 189 189 189 189. + 21 + 21 + 21 + 21. −.

Transcript of ejercicio 211 del libro de Baldor

Page 1: ejercicio 211 del libro de Baldor

Ejercicio 211 del libro de Baldor

�. (� + ��) =

(�)� + 6(�)�(2�) + 15(�)�(2�)� + 20(�)�(2�)� + 15(�)�(2�)� + 6(�)(2�)� + (2�)� =

�� + 6��(2�) + 15��(4��) + 20��(8��) + 15��(16��) + 6�(32��) + 64�� =

� = � + ����� + ����� + ������ + ������� + ������ + ��

�. (� � − �"�)� =

(2#�)� + 5(2#�)�(−3$�) + 10(2#�)�(−3$�)� + 10(2#�)�(−3$�)� + 5(2#�)(−3$�)� +(−3$�)� =

32#%& + 5(16#')(−3$�) + 10(8#�)(9$�) + 10(4#�)(−27$*) + 5(2#�)(81$%�)−243$%� =

32#%& + 80#'(−3$�) + 80#�(9$�) + 40#�(−27$*) + 10#�(81$%�)−243$%� =

� = �� �� − ��� +"� + ,�� " − ��+� �"� + +�� �"�� − ���"��

�. (-� + .�) =

(/�)� + 6(/�)�(0�) + 15(/�)�(0�)� + 20(/�)�(0�)� + 15(/�)�(0�)� + 6(/�)(0�)� + (0�)� =

/%� + 6(/%&)(0�) + 15(/')(0�) + 20(/�)(0*) + 15(/�)(0%�) + 6(/�)(0%�) + (0%') =

� = -�� + -��.� + ��-+. + ��-.� + ��-�.�� + -�.�� + .�+

4.4.4.4.---- (� ---- .,), ====

(3)3 + (3)� (−03) + (3)� (−03)� + (3)� (−03)� + (3)� (−03)� + (3)� (−03)� + (3) (−03)� + (−03)3 =

(3)3 + 7 (3)� (−03) + 21(3)� (−03)� + 35(3)� (−03)� + 35(3)� (−03)� + 21(3)� (−03)� + 7(3) (−03)� + (−03)3 =

R=R=R=R= 2187 2187 2187 2187 –––– 5103 5103 5103 5103 ., + 5103+ 5103+ 5103+ 5103.�� −2835283528352835.�� + 945+ 945+ 945+ 945.�+ − 189189189189.�� + 21+ 21+ 21+ 21.�� −.��

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5.5.5.5.---- (�-� − �.�)====

(2/�)� + (2/�)� (−30�) + (2/�)� (−30�)� + (2/�)� (−30�)� + (2/�)�(−30�)� + (2/�) (−30�)� + (−3y�)� =

(2/�)� + 6(2/�)� (−30�) + 15(2/�)� (−30�)� + 20(2/�)� (−30�)� + 15(2/�)�(−30�)� + 6(2/�) (−30�)� + (−3y�)� =

R= R= R= R= 64646464-�+ −�,-��.� + 2160+ 2160+ 2160+ 2160-��.+ − ����-�.�� + 4860 + 4860 + 4860 + 4860 -.� − ���-�.�� + 729+ 729+ 729+ 729.��

6.6.6.6.---- (� � -� + .�)�====

(%� 7�)� + (%

� /�)� (0�) + (%� 7�)�(8�)� + (%

� 7�)�(8�)� + (%� 7�)(8�)�

+ (0�)� =

(%� 7�)� + 5(%

� /�)� (0�) + 10(%� 7�)�(8�)� + 10(%

� 7�)�(8�)� + 5(%� 7�)(8�)� + (0�)� =

R=R=R=R= ��� 9�� + + + + �

� 9+ :� + + + + �� 9: + �� 9�:� + �

� 9�:�� + :��

,. (;� − �

<) =

( =�)� + ( =

�)� (− �>) + ( =�)� (− �

>)� + (=� )� (− �

>)�+ ( =�)� (− �>)� + ( =�) (− �

>)� + (− �>)�=

( =�)� + 6 ( =

�)� (− �>) + 15( =�)� (− �

>)� +20( =� )� (− �>)�+ 15( =�)� (− �

>)� + 6( =�) (− �>)� +

(− �>)�=

� = ;

,�� − �;�

�,< + �;�

�<� − ��;�

<� + ���;�

<� − �+;<� + ,��

<

+. (� − -�)+ =

(1)' + (1)3(−/�)+ (1)�(−x4)2+ (1)�(−x4)3+ (1)�(−x4)4 + (1)�(−x4)5+ (1)�(−x4)6+ (1)(−x4)7+ (−x4)8 =

(1)' + 8(1)3(−/�)+ 28(1)�(−x4)2+ 56(1)�(−x4)3+ 70(1)�(−x4)4 +56(1)�(−x4)5+ 28(1)�(−x4)6+ 8(1)( −x4)7+ (−x4)8 =

� =1 1 1 1 –––– 8x8x8x8x4444 + 28x+ 28x+ 28x+ 28x8888 –––– 56x56x56x56x12121212 + 70x+ 70x+ 70x+ 70x16161616 –––– 56x56x56x56x20202020 + 28x+ 28x+ 28x+ 28x24242424 –––– 8x8x8x8x28282828 + x+ x+ x+ x32323232

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�. ( ��- − �

�.)7 7 7 7 ====

( ��@) 7 + ( �

�@) 6 ( − ��A) + ( �

�@)�( − ��A)2 + ( �

�@ ) 4 (− ��A)3 + ( �

�@ ) 3 ( − ��A)4 + ( �

�@) 2 ( − ��A)5 + ( �

�@) (− �

�A)6 + (− ��A)7=

(− ��A) 7 + 7( �

�@) 6 (− ��A) + 21( �

�@)�(− ��A)2 + 35( �

�@ ) 4 (− ��A)3 + 35( �

�@ ) 3 ( − ��A)4 + 21(− �

�@) 2 ( − �

�A)5 + 7( ��@)(− �

�A)6 + (− ��A)7=

B = ��+��+,9,

− ������9: + �

�9�:� − ,��9�:� + ���

�9�:� − �,+9�:� + �,��

��9: − ��+,��+:,

10101010.... (((( 2222mmmm −

��

), =

( 2#), + 7( 2

#)�(− #�

2 ) + 21( 2#)�(− #�

2 )� + 35( 2#)�(− #�

2 )� + 35( 2#)�(− #�

2 )�

+21( 2#)�(− #�

2 )� + 7( 2#)(− #�

2 )� + (− #�

2 )3 =

R=R=R=R=��+ , − ���

� + �+ − ,� � + ��

� � − ��+ + + ,

�� �� − ��+

��

��. (-� + ")+ =

(/�)' + 8(/�)3(3#$) + 28(/�)�(#$)� + 56(/�)�(#$)� + 70(/�)�(#$)� +

56(/�)�(#$)� + 28(/�)�(#$)� + 8(/�)(#$)3 + (#$)' =

/�� + 8/�%#$ + 28(/%')(#�$�) + 56(/%�)(#�$�) + 70(/%�)(#�$�)

+56(/*)(#�$�) + 28(/�)(#�$�) + 8(/�)(#3$3) + (#'$') =

� = -�� + +-�� " + �+-�+ �"� + �-�� �"� + ,�-�� �"� + �-� �"�

+�+- " + +-� ,", + +"+

12.12.12.12.---- (3(3(3(3− <�

� )� =

(3)* + 9(3)'(− >D

� ) + 36(3)3 (− >D

� )� + 84(3)� (− >D

� )� + 126(3)� (− >D

� )� + 126(3)� (− >D

� )� + 84(3)� (− >D

� )� + 36(3)� (>D

� )3 + 9(3) (− >D

� )' + (− >D

� )*=

Page 4: ejercicio 211 del libro de Baldor

19683 − 59049 >D

� + 78732 >E

* − 61236 >F

�3 + 30618 >G

'% −10206 >HI

��� + 2268 >HD

3�* − 324 >HE

�%'3 + 27 >HF

���% − >HG

%*�'�=

R= 19683 R= 19683 R= 19683 R= 19683 − 19683196831968319683 �� + 8748 + 8748 + 8748 + 8748 �� − 2268 2268 2268 2268 � + 378+ 378+ 378+ 378 �+ – 42424242 ��� + + + + �+���

� − ����

�, + + + + ��

��� − ��+

��+�

13.13.13.13.---- (1(1(1(1− �9)�� =

(1)%& + 10(1)* (− %J) + 45(1)' (− %J)� + 120(1)3 (− %J)� + 210(1)� (− %J)� + 252(1)� (− %J)� +

210 (1)� (− %J)� + 120 (1)�(− %J)3 + 45(1)� (− %J)' + 10(1) (− %J)* + (− %J)%& =

1 − 10%J + 45 %

JD − 120 %JK + 210 %

JE − 252 %JL + 210 %

JF − 120 %JM + 45 %

JG − 10 %JN + %

JHI=

R= 1 R= 1 R= 1 R= 1 − ��9 + + + + ��

9� − ���9� + + + + ���

9� − ���9� + + + + ���

9 − ��� 9, + + + + ��

9+ − ��9� + + + + �

9��

��. O� � − �"�P =

(2#�)� + 6(2#�)�(−5$�) + 15(2#�)�(−5$�)� + 20(2#�)�(−5$�)� + 15(2#�)�(−5$�)� +6(2#�)(−5$�)� + (−5$�)� =

64#%� + 6(32#%&)(−5$�) + 15(16#')(25$%&) + 20(8#�)(−125$%�) + 15(4#�)(625$�&) +6(2#�)(−3125$��) + 15625$�& =

� = � �� − �� ��"� + ��� +"�� − ����� "�� + �,��� �"�� − �,��� �"�� +����"��

��. (�� − -

��),

=

43 + 7(�%)� Q− @

��R + 21(�

%)�(− @�

�)� + 35(�%)�(− @

��)� + 35(�

%)�(− @�

�)� + 21(�%)�(− @

��)� +

7(�%)(− @

��)� + (− @

��)3 =

16384 + 7(4096) Q− @�

�R + 21(1024) Q @%�

%&R + 35(256) Q− @��

%�R + 35(64) Q @���

�&R +

21(16) Q− @%&��

��R + 7(4) Q @�&*�

�&R − @%��'�

�� =

� = ��+� − ,�+-� + ����-�� − ���-�� + ��-�

��− ��-

���

+ ,-����

��− �-

��+���

Page 5: ejercicio 211 del libro de Baldor