In what sense does this have anything to do with "Tensor Analysis and Differential geometry"? I'm moving it to "number theory".
In any case, if 3x2= a2 for a and x integers, then we must have
[itex]a= x\sqrt{3}[/itex] which is impossible unless x= a= 0. It implies [itex]\sqrt{3}= a/x[/itex] but [itex]\sqrt{3}[/itex] is irrational.
The only integer solution to 3x2= a2 is x= a= 0.