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The $\triangle ABC$ and $\triangle AEF$ are in the same plane. Between them, the following conditions hold:
1. The midpoint of $AB$ is $E$.
2. The points $A,\,G$ and $F$ are on the same line.
3. There is a point $C$ at which $BG$ and $EF$ intersect.
4. $CE=1$ and $AC=AE=FG$.
Prove that if $AG=x$, then $AB=x^3$.
1. The midpoint of $AB$ is $E$.
2. The points $A,\,G$ and $F$ are on the same line.
3. There is a point $C$ at which $BG$ and $EF$ intersect.
4. $CE=1$ and $AC=AE=FG$.
Prove that if $AG=x$, then $AB=x^3$.