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% & = = ! − ! , # + -! # − ,! # + ,! # − # . (. +/ ) = (0 ) + 6(0 ) (1 ) + 15(0 ) (1 ) + 20(0 ) (1 ) + 15(0 ) (1 ) + 6(0 )(1 ) + (1 ) = 0 & + 6(0 &’ )(1 ) + 15(0 ( )(1 ) + 20(0 )(1 + ) + 15(0 )(1 & ) + 6(0 )(1 & ) + (1 &( )= =. + . / + . , / + . / + . / + . / +/ , 4. 4. 4. 4.- ( - / - ) - = (3) 3 + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 ) + (3) (−1 3 ) + (−1 3 ) 3 = (3) 3 + 7 (3) (−1 3 ) + 21(3) (−1 3 ) + 35(3) (−1 3 ) + 35(3) (−1 3 ) + 21(3) (−1 3 ) + 7(3) (−1 3 ) + (−1 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/ −/ 5. 5. 5. 5.- (. − / ) =

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%&� =

� = ��!�� − ���!,#� + -��!# − ��,�!�# + ,��!�#�� − ���#��

�. (.� + /�) =

(0�) + 6(0�)�(1�) + 15(0�)�(1�)� + 20(0�)�(1�)� + 15(0�)�(1�)� + 6(0�)(1�)� + (1�) =

0&� + 6(0&')(1�) + 15(0()(1 ) + 20(0 )(1+) + 15(0�)(1&�) + 6(0�)(1&�) + (1&() =

� = .�� + .��/� + ��.,/ + ��./ + ��.�/�� + .�/�� + /�,

4.4.4.4.---- (� ---- /-)- ====

(3)3 + (3) (−13) + (3)� (−13)� + (3)� (−13)� + (3)� (−13)� + (3)� (−13)� + (3) (−13) + (−13)3 =

(3)3 + 7 (3) (−13) + 21(3)� (−13)� + 35(3)� (−13)� + 35(3)� (−13)� + 21(3)� (−13)� + 7(3) (−13) + (−13)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/�� −/�

5.5.5.5.---- (�.� − �/�)====

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(20�) + (20�)� (−31�) + (20�)� (−31�)� + (20�)� (−31�)� + (20�)�(−31�)� + (20�) (−31�)� + (−3y�) =

(20�) + 6(20�)� (−31�) + 15(20�)� (−31�)� + 20(20�)� (−31�)� + 15(20�)�(−31�)� + 6(20�) (−31�)� + (−3y�) =

R= 64R= 64R= 64R= 64.�, −�-.��/� + 2160+ 2160+ 2160+ 2160.��/, − ����. /�� + 4860 + 4860 + 4860 + 4860 ./� − � �.�/�� + 729+ 729+ 729+ 729/��

6.6.6.6.---- (� � .� + /�)�====

(&� 7�)� + (&

� 0�)� (1�) + (&� 7�)�(8�)� + (&

� 7�)�(8�)� + (&� 7�)(8�)�

+ (1�)� =

(&� 7�)� + 5(&

� 0�)� (1�) + 10(&� 7�)�(8�)� + 10(&

� 7�)�(8�)� + 5(&� 7�)(8�)� + (1�)� =

R=R=R=R= ��� 9�� + + + + �

� 9, :� + + + + �� 9: + �� 9�: + �

� 9�:�� + :��

-. (;� − �

<) =

( =�) + ( =

�)� (− �>) + ( =�)� (− �

>)� + (=� )� (− �

>)�+ ( =�)� (− �>)� + ( =�) (− �

>)� + (− �>) =

( =�) + 6 ( =

�)� (− �>) + 15( =�)� (− �

>)� +20( =� )� (− �>)�+ 15( =�)� (− �

>)� + 6( =�) (− �>)� +

(− �>) =

� = ;

-� − �;�

�-< + �;�

�<� − ��;�

<� + ���;�

<� − �,;<� + -�

<

,. (� − .�), =

(1)( + (1)3(−0�)+ (1) (−x4)2+ (1)�(−x4)3+ (1)�(−x4)4 + (1)�(−x4)5+ (1)�(−x4)6+ (1)(−x4)7+ (−x4)8 =

(1)( + 8(1)3(−0�)+ 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=��,!- − ���

!� + �,! − -�!� + ��

� !� − ��, !, + -

�� !�� − !��,

��

��. (.� + !#), =

(0�)( + 8(0�)3(3$%) + 28(0�) ($%)� + 56(0�)�($%)� + 70(0�)�($%)� +

56(0�)�($%)� + 28(0�)�($%) + 8(0�)($%)3 + ($%)( =

0�� + 80�&$% + 28(0&()($�%�) + 56(0&�)($�%�) + 70(0&�)($�%�)

+56(0+)($�%�) + 28(0 )($ % ) + 8(0�)($3%3) + ($(%() =

� = .�� + ,.��!# + �,.�,!�#� + �.��!�#� + -�.��!�#� + �. !�#�

+�,.!# + ,.�!-#- + !,#,

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 − @

& �(��� =

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

��− ��.

���

+ -.����

��− �.

��,���

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