Question

El mcm de los numeros c= 12^20x18^10 y d= 6^30x8^10 es 2^x x 3^y Calcular x+y.

Answer 1

Respuesta:

Explicación paso a paso:

MCM(c, d)= 2^x •3^y

c= 12^20 • 18^10

c= (2^2•3)^20•(2 • 3^2)^10

c=(2^40•3^20)•(2^10•3^20)

c= 2^40•2^10•3^20•3^20

c=2^50 • 3^40

d=6^30 • 8^10

d=(2•3)^30 • (2^3)^10

d=2^30•3^30 • 2^30

d=2^30•2^30•3^30

d=2^60•3^30

MCM de:

(2^50•3^40) (2^60•3^30)

Factor:

(2^50•3^30)

Residuo:

(3^10) (2^10)

Factor:

2^10

Residuo:

(3^10) (1)

Factor:

3^10

Residuo:

(1) (1)

MCM=2^50•3^30•2^10•3^10

MCM= 2^50•2^10•3^30•3^10

MCM= 2^60 • 3^40

2^x • 3^y= 2^60 • 3^40

x=60

y= 40

x + y= 60 + 40

x + y= 100