δ=(2a^2)^2-4*a*27=4a^4- 108a>； =0, you can get a & gt=3 or a.

The root formula of X = (4a 4- 108a -2+ root sign) /54 = (a 4-27a-1+ root sign) /27.

This root can take the maximum value.

And because A 4-27a is increasing function in [3, positive infinity], (monotonicity can be proved by derivative).

So the bigger A is, the bigger X is, so X has no maximum.