Question

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Answer 1

Respuesta:

- 1

Explicación paso a paso:

✅

M.C.D(A,B) = 60

Entonces...

A = 25.60ⁿ

      ↓    ↓

A = $5^{2} . 2^{2n}.3^{n}. 5^{n}$

A = $2^{2n}.3^{n}.5^{2+n}$

...

B = 25ⁿ.60

B = $5^{2n}.2^{2}.3.5$

B = $2^{2}.3.5^{2n+1}$

Con eso...

A = $2^{2n}.3^{n}.5^{2+n}$

B = $2^{2}.3.5^{2n+1}$

Su M.C.D (son los datos comunes con los menores exponentes)

M.C.D = $2^{2}.3.5^{2+n}$

60 = $4.3.5^{n+2}$

60 = $12.5^{n+2}$

60 ÷ 12 = $5^{n+2}$

5¹ = $5^{n+2}$

*Teoría de exponentes

1 = n + 2

- 1 = n