EJERCICIO 9 y 10 DEL LIBRO DE BALDOR

EJERCICIO 9 (consta de 40 ejercicios)

1.1.1.1. 9a9a9a9a----3a+5a=3a+5a=3a+5a=3a+5a=

9a-3a=6a

6a+5a=11a

� = �

2. 2. 2. 2. ----8x+9x8x+9x8x+9x8x+9x----x=x=x=x=

-8x+9x=x

x-x=0

� = �

3. 3. 3. 3. 12mn12mn12mn12mn----23mn23mn23mn23mn----5mn=5mn=5mn=5mn=

12mn-23mn=-11mn

-11mn-5mn=-16mn

� = − ���

4.4.4.4. ----x+19xx+19xx+19xx+19x----18x=18x=18x=18x=

-x+19x=18x

18x-18x=0

� = �

5. 5. 5. 5. 19m19m19m19m----10m+6m=10m+6m=10m+6m=10m+6m=

19m-10m=9m

9m+6m=15m

� = ��

6.6.6.6.----11ab11ab11ab11ab----15ab+26ab=15ab+26ab=15ab+26ab=15ab+26ab=

-11ab-15ab=-26ab

-26ab+26ab=0

� = �

�. −���+���− ��� =

−5!"+9!" = 4!"

4!"−35!" = −31!"

� = − ��

#. −$%��&$ − ���'$+ ���'$ =

−24!"'(−15!"'( = −39!"'(

−39!"'(+39!"'( = 0

� = �

9.9.9.9. $

) +

) − ) =

2

3+

1

3=

3

3

R=R=R=R=

) − )

10.10.10.10.---- −

�� +

%� −

$� =

−+

,+

-

.−

-

(=

&-(',&-/

(/=

&-0

(/

R= R= R= R= & �

$��

11.11.11.11.

#�²2 +

%�²2 − �²2 =

3

8+

1

4=

3 + 2

8=

5

8

R=R=R=R=�

#�²2 − �²2

12.12.12.12. ––––a+8a+9aa+8a+9aa+8a+9aa+8a+9a----15a=15a=15a=15a=

-1+8+9-15=1

R=aR=aR=aR=a

13. 13. 13. 13. 7ab7ab7ab7ab----11ab+20ab11ab+20ab11ab+20ab11ab+20ab----31ab=31ab=31ab=31ab=

7ab-11ab+20ab-31ab=-15ab

R=R=R=R=----15ab15ab15ab15ab

14.14.14.14. 25x²25x²25x²25x²----50x²+11x²+14x²=50x²+11x²+14x²=50x²+11x²+14x²=50x²+11x²+14x²=

25-50+11+14=0

R=0R=0R=0R=0

15.15.15.15. ----xyxyxyxy----8xy8xy8xy8xy----19xy+40xy=19xy+40xy=19xy+40xy=19xy+40xy=

-1-8-19+40=12

R=12xyR=12xyR=12xyR=12xy

16. 16. 16. 16. 7ab+21ab7ab+21ab7ab+21ab7ab+21ab----abababab----80ab=80ab=80ab=80ab=

7+21-1-80=-53

R=R=R=R=----53ab53ab53ab53ab

17.17.17.17. ----25xy²+11xy²+60xy²25xy²+11xy²+60xy²25xy²+11xy²+60xy²25xy²+11xy²+60xy²----82xy²=82xy²=82xy²=82xy²=

-25+11+60-82=-36

R=R=R=R=----36363636xy²xy²xy²xy²

18.18.18.18.----72ax+87ax72ax+87ax72ax+87ax72ax+87ax----101ax+243ax=101ax+243ax=101ax+243ax=101ax+243ax=

-72+87-101+243=157

R=157axR=157axR=157axR=157ax

19. 19. 19. 19. ----82bx82bx82bx82bx----71bx71bx71bx71bx----53bx+206bx=53bx+206bx=53bx+206bx=53bx+206bx=

-82bx-71bx-53bx=-206bx

-206bx+206bx= 0

� = �

20. 20. 20. 20. 105105105105� ----464464464464� +58+58+58+58� +301+301+301+301� ====

105!++58!++301!+= 464!+

464!+-464!+= 0

R=0R=0R=0R=0

21.21.21.21.

$ x x x x ----

x + x + x + x +

% x x x x ----

� x =x =x =x =

2 3 4 5 2 30-20+15-12 = 13

1 3 2 5 2 60 60

1 3 1 5 3

1 1 1 5 5 m.c.m= 60

1 1 1 1

R=R=R=R=

���

22. 22. 22. 22.

y y y y ----

y + y + y + y +

� y y y y ----

$ y = y = y = y =

3 3 6 12 2 4-4+2-1 = 1

3 3 3 6 2 12 12

3 3 3 3 3

1 1 1 1 m.c.m= 12

R=R=R=R=

$)

23. 23. 23. 23.

� �$2 ----

� �$2 + + + +

�$2 ---- �$2 ====

5 6 3 2 18-5+10 23 −-

-= −

0

+/

5 3 3 3 30 30

5 1 1 5

1 1 1 m.c.m = 30

R=R=R=R=−�

� �$2

24.24.24.24. ---- �

� �2$ ----

� �2$ + + + + �2$----

# �2$ ====

x

=

−5

6!7( −

1

6!7( = −!7( + !7( = 0

−3

8!7( = −

3

8!7(

R=R=R=R=−

#�2$

25. 25. 25. 25. a+8aa+8aa+8aa+8a----11a+15a11a+15a11a+15a11a+15a----75a=75a=75a=75a=

8a+15a= 23a

-11a-75a= -86a

23a-86a = -64ª

R=R=R=R=----64a64a64a64a

26. 26. 26. 26. ----7c+21c+14c7c+21c+14c7c+21c+14c7c+21c+14c----30c+82c=30c+82c=30c+82c=30c+82c=

21c+14c+82c= 117c

-7c-30c= -37c

117c-37c = 80c

R=80cR=80cR=80cR=80c

27. 27. 27. 27. ----mn+14mnmn+14mnmn+14mnmn+14mn----31mn31mn31mn31mn----mn+20mn=mn+20mn=mn+20mn=mn+20mn=

14mn+20mn= 34mn

-mn-31mn-mn= -33mn

34mn-33mn= mn

R=mnR=mnR=mnR=mn

28. 28. 28. 28. �$y y y y ---- 7777�$y y y y ---- 93939393�$y + 51y + 51y + 51y + 51�$y + 48y + 48y + 48y + 48�$y=y=y=y=

!(y + 51!(y + 48!(y = 100!(y

- 7!(y - 93!(y = -100!(y

100!(y -100!(y=0

� = �

29. 29. 29. 29. ----a + a a + a a + a a + a ––––a +a a +a a +a a +a ----3a + 6a =3a + 6a =3a + 6a =3a + 6a =

-a - a – 3a = -5a

2a + 6a = 8a

8a – 5a=3a

� = $�

30.30.30.30.

$ x + x + x + x +

$

x x x x ----

�

� x + x + x + x +

$ x x x x –––– x=x=x=x=

-

( x +

(

+ x +

-

( x =

-/

9x

- 0

9 x – x =

-+

9x

10

6: −

13

6= −

3

6= −

1

2

� = −

$ �

31.31.31.31. ----2x + 2x + 2x + 2x +

%x + x + x + x +

%x + x x + x x + x x + x ----

�

� x=x=x=x=

+

.x +

-

.x + x =

;

.x

-2x - ,

9 x = -

-0

9x

;

.x -

-0

9x =−

-/

-(= −

,

9

� = −�

� �

32.32.32.32. 7777�� ---- 30303030�� –––– 41414141�� ----9 9 9 9 �� + 73+ 73+ 73+ 73��====

7!" + 73!" = 80!"

- 30!" – 41!" -9 !" = -80!"

80!" -80!" =0

� = �

33.33.33.33. ----��' ---- 7777��' − ��' − $���' + $���' ====

-!"'- - 7!"'- − 11!"'- − 20!"'- = -39 !"'-

-39 !"'- 26!"'- = -13!"'-

R=R=R=R=----13131313��'

34.34.34.34. a + 6a a + 6a a + 6a a + 6a –––– 20a + 150a 20a + 150a 20a + 150a 20a + 150a –––– 80a + 31a=80a + 31a=80a + 31a=80a + 31a=

a + 6a + 150a + 31a = 188a

– 20a – 80a =−100!

188! − 100! = 88!

R=88aR=88aR=88aR=88a

35.35.35.35. ----9b 9b 9b 9b ---- 11b 11b 11b 11b ----17b 17b 17b 17b –––– 81b 81b 81b 81b –––– b + 110b=b + 110b=b + 110b=b + 110b=

-9b - 11b -17b – 81b – b = -119b

-119b + 110b =-9b

R=R=R=R=----9b9b9b9b

36. 36. 36. 36. ----�$b + 15b + 15b + 15b + 15�$b + b + b + b + �$b b b b ---- 85858585�$b b b b ---- 131131131131�$b + 39b + 39b + 39b + 39�$b=b=b=b=

15!(b + !(b + 39!(b = 55!(b

-!(b - 85!(b - 131!(b = -217!(b

55!(b -217!(b = -162!(b

R=R=R=R=----162162162162�$bbbb

37. 37. 37. 37. #%�$� − �� �$� − ��%�$� − � ��$� + $ �$� + ���$� =

84<(: + 231<(: + 165<(: = 480<(:

−501<(: − 604<(: − 715<(: = −1820<(:

480<(: − 1820<(: = −940

R= R= R= R= −�%��$�

#. �

�� 2$ +

$

� 2$ −

%� 2$ + %� 2$====

5

6!+7( +

2

3!+7( +

4

1!+7( =

5

6!+7( +

12

18!+7( +

24

6!+7(

5

6!+7( +

12

18!+7( +

24

6!+7( =

15

18!+7( +

12

18!+7( +

72

18!+7( =

99

18!+7(

−1

4!+7( −

5

8!+7( = −

2

8!+7( −

5

8!+7( = −

7

8!+7(

99

18!+7( −

7

8!+7( = 4

5

8 !+7(

R=R=R=R=%�

# � 2$

�. %�� − # � + �� + % � − # � − � � + �� =

40! + 130! + 41! + 16! = 227!

−81! − 83! − 91! = −255!

−255! + 227! = −28!

R=R=R=R=----28a 28a 28a 28a

%�. −$ �2 + �$�2 − ���2 + #%�2 − �2 − �2 − $ �2====

−21!7 − 60!7 − 31!7 − !7 − 23!7 = −136!7

52!7 + 84!7 = 136!7

136!7 − 136!7 = 0

R=0R=0R=0R=0

EJERCICIO 10 (consta de 20 ejercicios)

1. 1. 1. 1. �= − �> + �= − %>====

7a + 6a = 13a

−9b − 4b = −13b

? = = − >

$. = + > − @ − > − @ + $@ − = =

a − a = 0

b − b = 0

−c − c = −2c + 2c = 0

R R R R = �

.�A − B − � + $�A − − B====

5x + 20x = 25x

−11y − y = −12y

−9 − 1 = −10

? = $�A − $B − �

%. − �C+ #D + � −C− D− �C− ====

−6m −m− 6m = −13m

8n − n = 7n

5 − 11 = −6

? = − C+ �D − �

5.5.5.5.----a+b+2ba+b+2ba+b+2ba+b+2b----2c+3a+2c2c+3a+2c2c+3a+2c2c+3a+2c----3b=3b=3b=3b=

-a+3a=2a

1b+2b-3b=0

-2c+2c=0

R=2aR=2aR=2aR=2a

6.6.6.6.----81x+19y81x+19y81x+19y81x+19y----30z+6y+80x+x30z+6y+80x+x30z+6y+80x+x30z+6y+80x+x----25y=25y=25y=25y=

-81x+80x+1=0

19y+6y-25y=0

-30z=-30z

R=R=R=R=----30z30z30z30z

7.7.7.7.15a15a15a15a2222----6ab6ab6ab6ab----8a8a8a8a2222+20+20+20+20----5ab5ab5ab5ab----31313131+=$----ab=ab=ab=ab=

15a2-8a2+a2=8a2

-6ab-5ab=-11ab-ab=-12ab

20-31=-11

R=8aR=8aR=8aR=8a2222----12ab12ab12ab12ab----11111111

8. 8. 8. 8. ----3a+4b3a+4b3a+4b3a+4b----6a+81b6a+81b6a+81b6a+81b----114b+31a114b+31a114b+31a114b+31a----aaaa----b=b=b=b=

-3a-6a=-9a+31a=22a-1a=21a

4b+81b=85b-114b=-29-1=-30b

R=21aR=21aR=21aR=21a----30b30b30b30b

9. 9. 9. 9. ----71a71a71a71a3333bbbb----84a84a84a84a4444bbbb2222+50a+50a+50a+50a3333b+84ab+84ab+84ab+84a4444bbbb2222----45a45a45a45a3333b+18ab+18ab+18ab+18a3333b=b=b=b=

-71a3b+50a3b=-21a3b-45a3b=-66a3b+18a3b=-48a3b

-84a4b2+84a4b2=0

R=R=R=R=----48a48a48a48a3333bbbb

10. 10. 10. 10. ----a+ba+ba+ba+b----c+8+2a+2bc+8+2a+2bc+8+2a+2bc+8+2a+2b----19191919----2c2c2c2c----3a3a3a3a----3333----3b+3c=3b+3c=3b+3c=3b+3c=

-1a+2a=a-3a=-2a

b+2b=3b-3b=0

-c-2c=-3c+3c=0

8-19=-11-3=-14

R=R=R=R=----2a2a2a2a----14141414

11. 11. 11. 11. mmmm2222+71mn+71mn+71mn+71mn----14m14m14m14m2222----65mn+m65mn+m65mn+m65mn+m3333----mmmm2222----115m115m115m115m2222+6m+6m+6m+6m3 3 3 3 ====

m2-14m2=-13m2-m2=-14m2-115m2=-129m2

71mn-65mn=6mn

m3+6m3=7m3

R=R=R=R=----129m129m129m129m2222+6mn+7m+6mn+7m+6mn+7m+6mn+7m3333

12.12.12.12. XXXX4444yyyy----xxxx3333 yyyy2222+x+x+x+x2222 yyyy----8x8x8x8x4444 yyyy----xxxx2 2 2 2 yyyy----10+x10+x10+x10+x3333 yyyy2222----7x7x7x7x3 3 3 3 yyyy2222----9+21x9+21x9+21x9+21x4444 yyyy----yyyy3333+50=+50=+50=+50=

X4 y-8x4 y=-7x4 y+21x4 y=14x4 y

-x3 y2+x3y2=0-7x3y2=-7x3y2

x2 y-x2 y=0

-10-9=-19+50=31

-y3=-y3

R=14xR=14xR=14xR=14x4444 yyyy----7x7x7x7x3333yyyy2222+31+31+31+31----yyyy3333

. ���' − 2�'$ − #G�' − ���' − �� + %2�'$ − �� − 2�'$ + �� + G�' +

�G�' ====

5!"'- − 5!"'- = 0

−37"'( + 47"'( − 7"'( = 0

−3H"'+ − 8H"'+ + H"'+ + 7H"'+ = 0

−50 − 65 + 90 = −25

R=R=R=R=----25252525

%. ��'$ − ��' − � + # − ��'$ + ���' − � + ��'$ − ���' ====

!I'( − 3!I'( + !I'( = −!I'(

−:I'+ + 5:I'+ − 5:I'+ = −:I'+

-5+8-6=-3

� = −��'$ − ��' −

15. 15. 15. 15. 0.3a+0.4b+0.5c0.3a+0.4b+0.5c0.3a+0.4b+0.5c0.3a+0.4b+0.5c----0.6a0.6a0.6a0.6a----0.7b0.7b0.7b0.7b----0.9c+3a0.9c+3a0.9c+3a0.9c+3a----3b3b3b3b----3c=3c=3c=3c=

0.3a-0.6a+3a=2.7a

0.4b-0.7b-3b=-3.3b

0.5c-0.9c-3c=-3.4c

R=2.7aR=2.7aR=2.7aR=2.7a----3.3b3.3b3.3b3.3b----3.4c3.4c3.4c3.4c

�.

$� +

2 + $� − 2 −

%� −

�2 +

%−

$=

1

2! + 2! −

3

4! = 1

3

4!

1

37 − 37 −

1

67 = −

17

67

3

4−

1

2=

1

4

� =

%� +

�

�2 +

%

�.

��$ − $��+

��$ −

�� + $�� − $�$

3

5<( +

1

10<( − 2<( = −1

3

10<(

−2<J −1

3<J + 2<J = −

1

3<J

� =

��$ −

��

#.−

%�$ +

$�2 −

�

�2$ + $

�$ −

%�2 +

�2$ −

2$ − $�2 =

21

3!( −

3

4!( = 1

7

12!(

1

2!7 −

3

4!7 − 2!7 = −2

1

4!7

−5

6b( +

1

6b( −

1

3b( = −b(

R=R=R=R= �

$=$ − $

%=> − >$

�. �. %A$B + +

#AB$ − �. �B −

$

�A$B − �. $AB$ +

%B − � =

4

10x(y −

2

5x(y = 0

31-6=25

3

8xy( −

2

10xy( =

7

40xy(

−6

10y+ +

1

4y+ = −

7

20y+

? = $� +�

%�AB$ −

�

$�B

$�.

$�=C& −

�

��>C&$ +

�=C& −

$�>C&$ − �. $=C& +

�>C&$

3

25aK&- +

3

5aK&- −

2

10aK&- =

13

25aK&-

−7

50bK&( −

1

25bK&( +

1

5bK&( =

1

50bK&(

? =

$�=C& +

��>C&$