In this study the classical Fekete-Szegö problem was investigated. Given f(z)=z+a2z2+a3z3+...  to be an analytic standartly normalized function in the open unit disk U={z ∈ C : |z|<1}. For |a3-μa22|, a sharp maximum value is provided through the classes of S*α,γ(β) order β and type α under the condition of μ≥1.