El conjunto solucion de la ecuacion (x + 4)³ - (x - 3)³ = 343 es :a)( - 3, 4)b){3, - 4}c){ - 3, - 4}d){1 / 4, 1 / 4}e) N?

Desarrollo :

<img src="https://tex.z-dn.net/?f=%20%28x%2B4%29%5E%7B3%7D%20-%20%28x-3%29%5E%7B3%7D%3D343" />

Sabemos que :

<img src="https://tex.z-dn.net/?f=%28a%2Bb%29%5E%7B3%7D%20%3D%20x%5E%7B3%7D%20%2B%20x%5E%7B3%7D%20%2B3ab%28a%2Bb%29" />

<img src="https://tex.z-dn.net/?f=%20%28a-b%29%5E%7B3%7D%20%3D%20a%5E%7B2%7D%20-%20b%5E%7B2%7D%20-3ab%28a-b%29" />

Resolvemos :

<img src="https://tex.z-dn.net/?f=%20%28x%2B4%29%5E%7B3%7D%20-%20%28x-3%29%5E%7B3%7D%3D343" />

<img src="https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20%2B%204%5E%7B3%7D%20%2B3%28x%29%284%29%28x%2B4%29-%28%20x%5E%7B3%7D%20-%203%5E%7B3%7D-3%28x%29%283%29%28x-3%29%20%29%3D343" />

<img src="https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20%2B64%2B12%20x%5E%7B2%7D%20%2B48x-%28%20x%5E%7B3%7D-27-9%20x%5E%7B2%7D%20%2B27x%20%29%3D343" />

<img src="https://tex.z-dn.net/?f=%20x%5E%7B3%7D%20%2B64%2B12%20x%5E%7B2%7D%20%2B48x-%20x%5E%7B3%7D%2B27%2B9%20x%5E%7B2%7D%20-27x%3D343%20" />

<img src="https://tex.z-dn.net/?f=21%20x%5E%7B2%7D%20%2B21x%2B91%3D343" />

<img src="https://tex.z-dn.net/?f=21%20x%5E%7B2%7D%20%2B21x-252%3D0" />

Dividimos entre 21 a ambos miembros :

<img src="https://tex.z-dn.net/?f=%20x%5E%7B2%7D%20%2Bx-12%3D0" />

Factorizamos :

[img = 10]

Entonces :

[img = 11]

[img = 12]

Por tanto los valores de "x" son :

[img = 13]

[img = 14]

Conjunto solución es :

CS = {3, - 4}.