Olympiad Math l Advance Algebric Problem l find all possible solutions of x?

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[carlosjimenez]

Mucho más sencillo!! Son las tres raíces cúbicas de 64, todas de módulo 4 y argumentos 0º, 120º y 240º, es decir, 4, 4(cos 120º + i sen 120º) = 2(-1 + i raíz(3)) y 4(cos 240º + i sen 240º) = 2(-1 - i raíz(3)). Fácil!!

[renesperb]

The solution x= 4 is very easy to see.If one looks at the graphs of y= x/4 and y= 16/x^2 it is also clear that this the only real solution.

[ДмитрийУдраскин]

And that the complex roots of verification were shy? Then 4 was not worth it.