Question

Si 45n × 21 tiene 144 divisores, calcula el valor de "n"

Answer 1

Respuesta:

n = 5

Explicación paso a paso:

N = numero

CD = cantidad de divisores

N = 45ⁿ × 21

CD = 144

Luego:

N = 45ⁿ × 21

N = (5 × 9)ⁿ × 3 × 7

N = (5 × 3²)ⁿ × 3 × 7

N = 5ⁿ × 3²ⁿ × 3 × 7

N = 5ⁿ × 3²ⁿ⁺¹ × 7

N = 3²ⁿ⁺¹ × 5ⁿ × 7¹

Formula:

CD = (2n + 1 + 1)(n + 1)(1 + 1)

CD = (2n + 2)(n + 1)(2)

CD = 2(n + 1)(n + 1)(2)

CD = 4(n + 1)²

144 = 4(n + 1)²

36 = (n + 1)²

(n + 1)² = 36

(n + 1) = √36

n + 1 = 6

n = 6 - 1

n₁ = 5,  si

(n + 1) = - √36

n + 1 = - 6

n = - 6 - 1

n₂ = - 7,  no

n = 5

Answer 2

Respuesta:

la respuesta es n=5