Question

Se x = $\sqrt{4+\sqrt{4+\sqrt{4} } }$ , então$x^{4}$ é igual a?

Answer 1

$x=\sqrt{4+\sqrt{4+\sqrt{4}}}\\\\\\x=\sqrt{4+\sqrt{4+2}}\\\\\\\boxed{x=\sqrt{4+\sqrt{6}}}$

$x^4~=~\sqrt{4+\sqrt{6}}^{\,4}\\\\\\x^4~=~\left(4+\sqrt{6}\right)^2\\\\\\x^4~=~(4+\sqrt{6}).(4+\sqrt{6})\\\\\\x^4~=~4^2+4\sqrt{6}+4\sqrt{6}+\sqrt{6}^2\\\\\\x^4~=~16+8\sqrt{6}+6\\\\\\\boxed{x^4~=~22+8\sqrt{6}}$

Resposta: Letra C