Question

Me ayudan por favor (paso a paso)

Answer 1

Respuesta:

$\bold{ E = \frac{1}{2}}$

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Producto notable:

$\bold{ (a+b)(a-b)= a^2 - b^2 }$

Resolución:

$\bold{ \frac{x^{12} -1}{x^3 -1} = (x^m+1 )(x^n+1)}$

$\bold{ \frac{(x^6+1)(x^6-1)}{x^3 -1} = (x^m+1 )(x^n+1)}$

$\bold{ \frac{(x^6+1)(x^3+1)(x^3 -1)}{(x^3 -1)} = (x^m+1 )(x^n+1)}$

$\bold{ (x^6+1)(x^3+1)= (x^m+1 )(x^n+1)}$

Entonces:

$\bold{\to \: \: \: m \: = \: 6}$

$\bold{ \to \: \: \: n \: = \: 3 }$

Calcular el valor de:

$\bold{ E = \frac{1}{m} + \frac{1}{n}}$

$\bold{ E = \frac{1}{6} + \frac{1}{3}}$

$\bold{ E = \frac{1}{6} + \frac{2}{6}}$

$\bold{ E = \frac{3}{6}}$

$\bold{ E = \frac{1}{2}}$