Trabajo Colaborativo 3 Geometría Analítica

EJERCICIOS PLANTEADOS

Resuelva las siguientes ecuaciones:

5t-22 _ - 11____ = 5

T2-6t+9 t2-3t t

R/. 5t-22 _ - 11____ = 5

(t-3) (t-3) t (t-3) t

5t-22 _ - 11____ - 5__ =0

(t-3)2 t (t-3) t

(5t-22)(t)-11(t-3)-5(t-3)2 = 0

T (t-3)2

5t2-22t-11t+33-5(t2-6t+9) = 0

T (t-3)2

5t2-22t-11t+333-5t2+30t-45 = 0

T (t-3)2

-3t-12____ = 0

T (t-3)2

-3t-12= o* t (t-3)2

-3t-12= o

-3t =12

T= 12/-3 T= -4

1/(X^2+3x+2)-1/(1-x)=2/(X^2-4)

R/:

1/(X-2) (X+1) – 1/-(1-X) – 2/(X+2) (X-2) = O

1/(X-2) (X+1) + 1/(X+1) – 2/(X+2) (X-2) = O

1(X-1) (X-2) + 1(X+2) (X+1) (X-2) – 2 (X+1) (X-1) / (X+2) (X+1) (X-1) (X-2) =0

(X2-3X+2) + (X2+3X+2) (X-2) – 2X2+2X-2X+2 / (X+2) (X+1) (X-1) (X-2) = O

X2-3X+2 +X3+3X2+2X-2X2-6X+4-2X2-2/ (X+2) (X+1) (X-1) (X-2) = O

X2-3X+2 +X3+X2-4X+4-2X2+2/ (X+2) (X+1) (X-1) (X-2) = O

X3- 7X = 0

X (X2-7) = 0

X2-7 = 0/X

X2-7 = 0

X2 = 0 +7

X2 = 7

X= √7

3[1/2-(x-1)/(x+1)]=1/4 [9/(x+1)-1]

3[x+1-2(x-1)/(2 (x+1) )]=1/4 [(9-(x+1))/(x+1)]

3[x+1-2x+2/(2 (x+1) ]=1/4 [9-x-1/(x+1)]

3[-x+3)/(2 (x+1) )]=1/4 [(8-X)/(x+1)]

-3x+9)/(2 (x+1) )]=1/4 [(8-X)/4(x+1)]

FACTORIZANDO

-3x+9)/(2 (x+1) )]=1/4 [(8-X)/4(x+1)]

〖-12x〗^2+24x+36=〖-2x〗^2+14x+16

〖-12x〗^2+2x^2+24x-14x+36-16=0

〖-10x〗^2+10x+20=0

〖-10(x〗^2-x-2)=0

〖(x〗^2-x-2)=0/-10

〖(x〗^2-x-2)=0

(x-2)(x+1)=0

X- 2 = 0 X+1 = O

X= 2 Ó X= -1

D. (m^2-n^2 ) x^2+2(m^2-n^2 )x+(m^2-n^2)= 0

Sacando el término factor común en la ecuación se tiene:

(m^2-n^2)┤*[x^2+2x+1]=0

(m^2-n^2)* (x+1)(x+1)┤=0

(m^2-n^2 ┤)*(〖x+1)〗^2 ┤=0

(〖x+1)〗^2 ┤=0/(m^2-n^2 )

(〖x+1)〗^2 ┤=0

√((x+1)^(2 ) ) =√0

x+1=0

x=-1

Luego la solución de la ecuación es X=-1

E. 24/(10+m)+1=24/(10-m)

24/(10+m)+ 1/1=24/(10-m)

(24(1)+1(10+m))/((10+m))=24/(10-m)

(24+10+m)/(10+m)=24/(10-m)

(34+m)/(10+m)=24/(10-m)

(34+m)(10-m)=24(10+m)

340-34m+10m-m^2=240-24m

340-24m-m^2=240-24m

340-24m-m^2-240+24m=0

100-m^2=0

(10-m)(10+m)=0

m=10 ó m=-10

La diferencia entre la tercera parte de un capital A y la cuarta parte de un capital B es $2.000. Y la diferencia entre el 5% del capital A y el 6% del capital B es de $30. ¿Cuáles son los capitales?

Solución

A –B = 2000

3 4

A = 3 2000 + B)

4

A = 6000 + 3 B

4

0,05A - 0, 06 B = 30

A = 30 + 0,06 B

0, 05

A= 600 + 1,2B

600 + 1,2 B = 6000 + 0,75 B

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