A = 4x2 - 4x + 999 + 4x(1+ x3) = 4x[x - 1 + (1+x3) ] + 999
= 4x( x -1+1+x3) + 999
= 4x( x + x3) + 999
= 4x2 + 4x4 + 999
= (2x)2 + (2x2)2 + 999
Vì (2x)2 + (2x2)2 luôn > 0 với mọi x
=> (2x)2 + (2x2)2 + 999 > 999
Vậy Amin= 999 <=> x = 0