According to the meaning of the question, the polynomial about x is a quadratic polynomial, that is, the coefficient of the cubic term of x is zero and the coefficient of the square term of x is non-zero.

So (the square of a -4) =0, find out a=2 or a =-2;

And because a+2 is not equal to 0, A is not equal to-2;

So a has only a unique value, that is, a = 2；;

The square of A+1/a +a =4+ 1/4+2=6.25.