Algebra, Trigonometria y Geometria
Juan Carlos Enríquez (c.c. 87.574.749)
Leandro Ramón Ramírez (c.c. 86.014.658)
Ricardo Rey Guzmán Pérez (c.c. 12.209.543)
Tutor: John Gabriel ÁngelOsorio
UNIVERSIDAD NACIONAL ABIERTA Y A DISTANCIA – UNAD
ESCUELA DE CIENCIAS BASICAS, TECNOLOGIA E INGENIERIA
ALGEBRA, TRIGONOMETRIA Y GEOMETRIA ANALITICA
Neiva, 3 de octubre de 2011
1.Solución de las ecuaciones:
a.
5t-22t2-6t+9-11t2-3t=5t
5t-22t2-6t+9=5t+11t2-3t
5t-22t2-6t+9=5t+11t2-3t
5t-22t2-6t+9=5t2-3t+11tt(t2-3t)
5t-22t2-6t+9=5t2-15t+11tt(t2-3t)5t-22t2-6t+9=5t2-4tt(t2-3t)
5t-22(t-3)(t-3)=t(5t-4)t(t2-3t)
5t-22(t-3)(t-3)=5t-4t(t-3)
5t-22t-3=5t-4t
t5t-22=(5t-4)(t-3)
5t2-22t=5t2-15t-4t+12
5t2-22t-5t2+15t+4t-12=0
-3t-12=0
-3t=12
t=-123t=-4
b.
1x2+3x+2-11-x=2x2-4
1(x+2)(x+1)-11-x=2(x+2)(x-2)
x+2(x+2)(x+1)-x+21-x=2x-2
1(x+1)-x+21-x=2x-2
(1-x)-(x+2)(x+1)(x+1)(1-x)=2x-2
1-x-(x2+x+2x+2)x-x2+1-x=2x-21-x-x2-x-2x-2x-x2+1-x=2x-2
-x2-4x-11-x2=2x-2
x-2-x2-4x-1=2(1-x2)
-x3-4x-x+2x2+8x+2=2-2x2
-x3-4x-x+2x2+8x+2-2+2x2=0
-x3+7x=0
x(x2-7)=0
x=0; x=7; x=-7
c.
312-x-1x+1=149x+1-142-4x-1x+1=139x+1-1
2-4x-1x+1=3x+1-13
2-4x-1x+1=3x+1-13
4(x-1)x+1+3x+1=2+13
4x-4+3x+1=6+13
4x-1x+1=73
34x-1=7(x+1)
12x-3=7x+7
12x-7x=7+3
5x=10
x=105
x=2
d.m2-n2x2+2m2-n2x+m2-n2=0
x=-2m2-n2±(2m2-n2)2-4m2-n2m2-n22m2-n2
x=-2m2-n2±4m2-n22-4m2-n222m2-n2
x=-2m2-n2±02m2-n2
x=-2m2-n22m2-n2
x=-1
e.
2410+m+1=2410-m
24(10-m)10+m+(10-m)=242410-m+(10-m)(10+m)10+m=24
2410-m+(10-m)(10+m)=24(10+m)
240-24m+100+10m-10m-m2=240+24m
240-24m+100+10m-10m-m2-240-24m=0
-m2-48m+100=0
(-1)(-m2-48m+100)=(-1)0
m2+48m-100=0(m+50)(m-2)=0
m=-50
m=2
2. La diferencia entre la tercera parte de un capital A y la cuarta parte de un capital B es $ 2000. Y la diferencia entre el 5% del capital A y el 6% del capital B es...
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