Como es la resolución, ayúdenme ?

Pasos :

<img src="https://tex.z-dn.net/?f=4%5E%7B%5Csqrt%7Bx%2B1%7D%7D-2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D%3D0" />

Sumar <img src="https://tex.z-dn.net/?f=2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D" />a ambos lados

<img src="https://tex.z-dn.net/?f=4%5E%7B%5Csqrt%7Bx%2B1%7D%7D-2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D%2B2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D%3D0%2B2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D" />

Simplificar

<img src="https://tex.z-dn.net/?f=4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3D2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D" />

Convertir<img src="https://tex.z-dn.net/?f=4%5E%7B%5Csqrt%7Bx%2B1%7D%7D" /> a base 2

<img src="https://tex.z-dn.net/?f=4%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3D%5Cleft%282%5E2%5Cright%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D" />

<img src="https://tex.z-dn.net/?f=%5Cleft%282%5E2%5Cright%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3D2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D" />

Aplicar las leyes de los exponentes : <img src="https://tex.z-dn.net/?f=%5Cleft%28a%5Eb%5Cright%29%5Ec%3Da%5E%7Bbc%7D" />

<img src="https://tex.z-dn.net/?f=%5Cleft%282%5E2%5Cright%29%5E%7B%5Csqrt%7Bx%2B1%7D%7D%3D2%5E%7B2%5Csqrt%7Bx%2B1%7D%7D" />

<img src="https://tex.z-dn.net/?f=2%5E%7B2%5Csqrt%7Bx%2B1%7D%7D%3D2%5E%7B%5Csqrt%7Bx%2B1%7D%2B2%7D" />

Si[img = 10] , entonces[img = 11]

[img = 12] ← este procedimiento es muy largo y demoraremucho, asíque resumido sale :

x = 3

Saludos!