Question

Ayuda porfa doy corona

Answer 1

Respuesta:

b - a = 4

Explicación paso a paso:

DN = cantidad de divisores de N

DM = cantidad de divisores de M

N = 2ᵃ × 3ᵇ

M = 15ᵃ × 2ᵇ

DN = 12

DM = 24

b - a = ?

Formula:

DN = (a + 1)(b + 1)

12 = (a + 1)(b + 1)

Luego:

M = 15ᵃ × 2ᵇ

M = (3 × 5)ᵃ × 2ᵇ

M = 3ᵃ × 5ᵃ × 2ᵇ

M = 2ᵇ × 3ᵃ × 5ᵃ

Formula:

DM = (b + 1)(a + 1)(a + 1)

24 = (b + 1)(a + 1)(a + 1)

24 = (a + 1)(b + 1)(a + 1)

Reemplazar:

24 = 12(a + 1)

2 = a + 1

2 - 1 = a

1 = a

a = 1

También:

12 = (a + 1)(b + 1)

12 = (1 + 1)(b + 1)

12 = 2(b + 1)

6 = b + 1

6 - 1 = b

5 = b

b = 5

Luego:

b - a = 5 - 1

b - a = 4