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8/18/2019 Actividad 1 de Fundamentos Matematicos
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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"
8/18/2019 Actividad 1 de Fundamentos Matematicos
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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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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)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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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*.−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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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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.
8/18/2019 Actividad 1 de Fundamentos Matematicos
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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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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)). ( 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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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)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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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.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
8/18/2019 Actividad 1 de Fundamentos Matematicos
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/.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