Thank you alot. Only a a little modification of code give me the result (Mathematica seems cannot recognize power in the PlotLabel). It is smart of you to use //InputForm!
Manipulate[
Plot[{x^3 + a*x + b,
Sqrt[x^3 + a*x + b], -Sqrt[x^3 + a*x + b]}, {x, -5, 5},
PlotStyle -> {{Thin, Blue}, {Thick, Red}, {Thick, Red}},
PlotRange -> {{-5, 5}, {-20, 20}},
PlotLabel -> Style[Chop[y ^2 == x^3 + a x + b ] , 18],
AxesStyle -> Directive[14],
ImageSize -> Large], {{a, 4, Style["A", Italic, 18]}, -5, 5,
0.1}, {{b, -3, Style["B", Italic, 18]}, -5, 5, 0.1},
Initialization :> {a = 4, b = -3}]