If real numbers a and B satisfy 1 / 2A AB + B & sup2; + 2 = 0, then the value range of a is I know to use formula method to calculate, but I don't know why I calculate a greater than or equal to - 2 and a greater than or equal to 4, which is different from the answer. The answer is a > = 4 or a

If real numbers a and B satisfy 1 / 2A AB + B & sup2; + 2 = 0, then the value range of a is I know to use formula method to calculate, but I don't know why I calculate a greater than or equal to - 2 and a greater than or equal to 4, which is different from the answer. The answer is a > = 4 or a

I don't know how you do it. I do
1/2a-ab+b²+2=0
b²-ab+1/2a+2=0
△=a²-4(2+1/2a)≥0
a²-2a-8≥0
(a+2)(a-4)≥0
A ≤ - 2, or a ≥ 4,