Do gen analysis this equation...............................................(a^6+5a^3+8 )

First of all its not an equation since equation consists of an equal to sign and two parts L.H.S. and R.H.S. This can be regarded as an expression which has least value equal to 7/4 at a=-(5/2)^1/3 this can be found by completing the square in the expression:a^6 + 2×(5/2)×(a)^3 + 25/4 +8 - 25/4= {(a)^3 + 5/2}^2 + 7/2As {(a)^3 + 5/2}^2 ≥ 0therefore {(a)^3 + 5/2}^2 + 7/2 ≥ 7/2Equality occurs at a= - (5/2)^1/3The maximum value of this expression can be ∞ as no constraints on aThank you