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8/18/2019 Actividad 1 de Fundamentos Matematicos

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Ciudad illavicencio !Meta" #ctubre " $% de $&1'

EJERCICIOS 1-1

1. Establezca si cada una de las

siguientes igualdades es válida o

no. Reemplace cada proposiciónalsa por una !ue sea correcta.

a" 3 x+4 x=7 x #verdadera"b" (3 x) (4 x )=7 x #alsa". (3 x ) (4 x )=12 x

2

c" 2 (5−4 y )=10−4 y #alsa". 2 (5−4 y )=10−8 y

d" −( x+ y )=− x+ y #alsa". −( x+ y )=− x− y

e" 5 x−(2−3 x )=2 x−2 #alsa". 5 x−(2−3 x )=8 x−2" 5−2 x=3 x #alsa". 5−2 x=5−2 x

g" −3 ( x−2 y )=−3 x−6 y #alsa". −3 ( x−2 y )=−3 x+6 y

$" (−a ) (−b ) (−c )

(−d ) =−(

abc

d ) #alsa".

(−a ) (−b ) (−c )−d

=abc /d

i"a

b

c

=(ac)/b

#verdadera"

%" a−(b−c )=(a+c )−b #verdadera"&" (− x ) (− y )=− xy #alsa". ( – x ) (− y )= xy

l" −a−b

=a/b #verdadera"


3/12

m" 0

x=0 para todos los n'meros

reales (

#)-*+" simpli,!ue las siguientes

e(presiones.

). 5−(−3 )=5+3=8

. −7−(−3 )=−7+3=−4

. 5(−3)=−15

/. (−3 ) (−7 )=21

*. 8

−2=−4

0. (−9 )/ (−3 )=3

. −(2−6 )=4

2. −(−4−3 )=7

1+. (3 ) (−2 ) (−4 )=24

11. (−5 ) (−3 ) (−2 )=−30

1). 3 (1−4 )=−9

1. 2 (−2−3 )=2 (−5 )=−10

1. −2 (−4−2 )=−2 (−6 )=12

1/. −4 (3−6 )=−4 (−3 )=12

1*. −6−2 (−3−2 )=−6−2 (−5 )=−6+10=4

10. 3 ( x+2 y )=3 x+6 y

1. 4 (2 x+ z )=8 x+4 z

12. 2 (2 x− y )=4 x−2 y

)+. 3 (4 z−2 x )=12 z−6 x


4/12

)1. −( x−6 )=− x+6

)). −(− x−3 )= x+3

). 3 ( x−4 )=3 x−12

). 2 (− x−3 )=−2 x+6

)/. −2 (− x−2 )=2 x+4

)*. −4 ( x−6 )=−4 x+24

)0. − x ( y−6 )=− xy+6 x

). − x (− y−6 )= xy+6 x

)2. 2 ( x− y )+4 x=2 x−2 y+4 x=6 x−2 y

+. 3 y+4 ( x+2 y )=3 y+4 x+8 y=11 y+4 x

1. −2 z−3 ( x−2 z )=−2 z−3 x+6 z=4 z−3 x

). −4 x−2 (3 z−2 x )=−4 x−6 z+4 x=−6 z

. ( x+ y )+4 ( x− y )= x+ y+4 x−4 y=5 x−3 y

. 3 ( y−2 x )−2 (2 x−2 y )=3 y−6 x−4 x+4 y=7 y−10 x

/. 5 (7 x−2 y )−4 (3 y−2 x )=35 x−10 y−12 y+8 x=43 x−22 y

*. 4 (8 z−2t )−3 (−t −4 z )=32 z−8 t +3 t +12 z=44 z−5 t

0. x (− y ) (− z )= xyz

. (− x ) (− y ) (− z )=− xyz

2. (−2 ) (− x ) ( x+3 )=2 x ( x+3 )=2 x2+6 x

+. (− x ) (− y ) (2−3 z )= xy (2−3 z )=2 xy−3 xyz

1. 2 (−a ) (3−a )=−2a (3−a )=−6a+2a2

). (−37 p ) (2q ) (q− p )=74 pq (q− p )=74 p q2−74 p 2q

. x (−2 ) (− x−4 )=−2 x (− x−4 )=2 x2+8 x

. (−2 x ) (−3 ) (− y−4 )=6 x (− y−4 )=−6 xy−24 x

/. − x ( x−2 )+2 ( x−1 )=− x2+2 x+2 x−2=− x2+4 x−2


5/12

*.−2 (−3 x ) (−2 y+1 )− (− y ) (4−5 x )=6 x (−2 y+1 )−(−4 y+5 xy )=−12 xy+6 x+4 y−5 xy=6 x−17

0. 2 x+5−2 ( x+2 )=2 x+5−2 x−4=1

. 3 x−t −2 ( x−t )=3 x−t −2 x+2 t = x+t

2. 2 ( x− y )− x=2 x−2 y− x= x−2 y

/+. 4 x ( x+ y )− x2=4 x2+4 xy− x2=3 x2+4 xy

/1. 4 [2 ( x+1 )−3 ]=4 [2 x+2−3 ]=4 [2 x−1 ]=8 x−4

/). x [3 ( x−2 )−2 x+1 ]= x [3 x−6−2 x+1 ]= x [ x−5 ]= x2−5 x

/. x [−3 (−4+5 )+3 ]= x [−3 (1 )+3 ]= x [−3+3 ]= x [−3+3 ]= x [0 ]=0

/.4 [ x (2−5 )−2 (1−2 x ) ]=4 [ x (−3 )−2+4 x ]=4 [−3 x−2+4 x ]=4 [ x−2 ]=4 x−8

//. x−1 ( x+2 )= x0+2 x−1=1+2 x−1

/*. x−1 (2 x−1 )=2 x0− x−1=2− x−1

/0. (−2 x )−1 (3 x−1 )=

3 x−1−2 x

= 3 x

−2 x−

1

−2 x=−32

+ 1

2 x

/. (−3 x )−1 (6+2 x )=6+2 x

−3 x = 6

−3 x+ 2 x−3 x

=−2 x −2

3

/2. ( xy)−1 ( x+ y )=

x+ y xy

= x

xy+ y

xy=

1

y+1

x

*+. (− xy)−1 (2 x−3 y )=

2 x−3 y− xy

= 2 x

− xy− 3 y

− xy=−2 y +

3

x

EJERCICIOS 1-)

1. Establezca si cada una de las

siguientes igualdades es válida o


6/12

no. Reemplace cada proposición

alsa por una !ue sea correcta.

a"

3

x

+4

x

=7

x #verdadera"b"

x

3+

x

4=

x

7 #alsa". x

3+

x

4=

4 x+3 x12

=7 x

12

c" a

b+c

d=

a+cb+d #alsa".

a

b+

c

d=

ad+cbbd

d" ab∗(

c

d∗e

f )=

ace

bdf #verdadera"

e" (

ab

c

d

)/ e

f =

adf

bce

#verdadera"

" ab/(

c

d /e

f )=

adf

bce#alsa". a

b/(

c

d /e

f )=

ade

bcf

g"

1

a

+1

b

= 1

a+b #alsa".

1

a

+1

b

=b+a

ab

$" x

x+ y=

1

1+ y #alsa". x

x+ y=

x

x+ y

i"6

7∗8

9=6∗9+7∗8

7∗9 #alsa".6

7∗8

9=6∗87∗9

%" 1+2+3+4+52+4+6+8+10

=1

2 #verdadera"

#)-/" Evalu3 cada una de las

siguientes e(presiones. Escriba las

respuestas en t3rminos más simples.


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).2

9∗6

5=

12

45= 4

15

. (

8

3

)(

15

4

)=120

12=10

.

3

4∗8

5∗4

9= 96

180= 8

15

/.

2

5∗3

6∗10

7= 42

210=

1

5

*. (3 x

25 )( 25

9 x )= 75 x

225 x=1

3

0. (14 x

15 y )(25 y24 )=350 xy360 y =35 x36

. 7 x2( 6 y21 x )=42 x

2

y

21 x =2 xy

2. (−2 x3 y ) (−5 xy )=10 x

2

y

3 y =

10 x2

3

1+.( 1811 )( 833 )

=594

88=

27

4

11.( 143 )( 615 )

=210

18=

35

3

1).

4

9

2

3∗8

=

4

9

16

3

= 12

144= 1

12


8/12

1.

12

25∗15

7

20

7

=

180

175

20

7

=1260

3500= 9

25

1.(7 x10 )( 21 x5 )

= 35 x

210 x=

1

6

1/.2 x

3 xy

5

=10 x

3 xy= 10

3 y

1*.

4

89 x

=36 x

8

=9 x

2

10.( 38 x )( 4 x15 )

= 45

32 x2

1.

3 x2

20∗4 y

6 xy

25

=

12 x2

y

20

6 xy

25

=300 x

2

y

120 xy =

5 x

2

12.

5 x

2∗3 y

4

x2

y

12

=

15 xy

8

x2

y

12

=180 xy

8 x2

y=

45

2 x

)+.

8 xy

2 x

3∗2 x

5 y

= 8 xy

4 x2

15 y

=120 x y

2

4 x2 =

30 y2

x

)1.

6 x2

4 x

y ∗3 y2

2

= 6 x

2

12 xy2

2 y

=12 x

2

y

12 xy2 =

x

y


9/12

)). ( 8

9t

1

3 st )∗s4

=

24 st

9t ∗s

4=24 s

2

t

36 t =

2 s2

3

). ( 3

4 xy

x

y )∗2 xy9

=

3 y

4 x2

y∗2 xy

9=

6 xy2

36 x2

y=

y

6 x

).

(

2

x

z

2

)4 z=

4

xz4

z

= 4 z4 xz

=1 x

)/. ( 2 xt

3

x

4 t )

2 t

3

=

8 x t 2

3 x

2 t

3

=24 x t

2

6 xt =4 t

)*.

2

z

z

2

4

z

=

2

z

z2

8

=16

z3

)0.

2 xt

3

x

4 t 2 t

3

=

2 xt

3

3 x

8t 2

=16 x t

3

9 x =

16 t 3

9

). 1

6−1

2=

2−612

=−412

=−13


10/12

)2. 1

10+ 1

15=3+230

= 5

30=1

6

+. 4 x

5−

x

10=8 x− x10

=7 x

10

1. 1

x + 12 x

=2+12 x

= 32 x

). x

2+

x

3=

3 x+2 x6

=5 x

6

. y

2 x+ 1

3 x=3 y+26 x

. a

6 b−

a

2b=

a−3a6b

=−2a6b

=−a3b

/. a

6 b+ 2a9b

=3a+4a18b

= 7a18b

*. 7

6 x +

3

4 x2=

14 x+9

12 x2

0. 3 y

10 x2−

1

6 x=

9 y−5 x

30 x2

. x

p2+

y

pq=

qx+ py

p2

q

2. x

y +

y

z +

z

x=

x2

z+ x y 2+ y z 2

xyz

+. x

y−

y

x= x

2− y2

xy

1. x

2

3 y +4 y=

x2+12 y 2

3 y

).

1

6+

(

2

x+ x

2

)=

1

6+

(

4+ x2

2 x

)= x+12+3 x2

6 x =

3 x2+ x+126 x

. 1

6−( 2 x− x2 )=16−(4− x

2

2 x )= x−12+3 x2

6 x =

3 x2+ x−126 x


11/12

.a

3b−2( ab− b2a )= a3b−2(2a

2−b2

2ab )= a3b−(2a2−b2

ab )=a2−6a2+3b2

3ab =

−5a2+3b2

3ab

/. x2+ 2

x

6

x

=

x2

+42 x

6

x

= x

3+4 x12 x

= x

2+412

*.

x

9 y+ 1

6 xy

1

3 xy

=

2 x2+3

18 xy

1

3 xy

=6 x

3

y+9 xy18 xy

=2 x

2+36

0.

1

4−

2

5

1

2−1

5

=

5−8

20

5−210

=

−3

20

3

10

=−3060

=−12

. (2

3+ 1

12 )∗( 710+ 14 )=( 8+112 )∗( 14+520 )=( 912 )∗(1920 )=171240=5780

2.

1

2−1

3

1

4+1

5

=

3−26

5+420

=

1

6

9

20

=20

54=10

27

/+.

8

5+2

3

2+4

7

=

24+1015

14+47

=

34

15

18

7

=238

270=

119

135

/1.

1

3−1

4

1

5−1

6

=

4−312

6−530

=

1

12

1

30

=30

12=5

2

/).2−3

4

3+1

8

=8−34

24+18

=54

25

8

= 40

100=

2

5


12/12

/.7 x−

2 x

3

15 y− y

3

=

21 x−2 x3

45 y− y3

=

19 x

3

44 y

3

= 57 x

132 y=

19 x

44 y

/.

1

2 x− 1

3 x

1

4 y−

1

5 y

=

3−26 x

5−420 y

=

1

6 x

1

20 y

=20 y

6 x =

10 y

3 x

//.( 2a3b )( 4 b5 )+a

2b+ b

15

=

8a

15+a

30b+b15

=

8a+15a15

31b

15

=

23a

15

31b

15

=23a

31b

/*. (5 p

2q

)( p

3

)+ p

2

8q

4 p+ p

12

=

5 p2

6q

+ p

2

8q48 p+ p

12

=

20 p2+3 p2

24q49 p

12

=

23 p2

24q49 p

12

= 276 p2

1176 pq=23 p

98q

/0.

a

b+2a

3b

[ 3 x

8

x

9−

1

4 ]=

3 a+2a3b

[ 3 x

8

4 x−936 ]

=

5a

3b

[ 108 x32 x−72 ]=

160ax−360a324 bx

/.

xy6

[ 2

3

x

6−

3 x

4 ]=

xy6

[ 2

3

4 x−18 x24

]=

xy6

[ 2

3

−14 x24 ]

=

xy6

[−4842 x ]=

42 x2

y

288=

7 x2

y

48

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