Simply connected symplectic 4-manifolds with b₂+ =1 and c₁² =2

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In this article we construct a new family of simply connected symplectic 4-manifolds with b₂+ =1 and c₁² =2 which are not diffeomorphic to rational surfaces by using rational blow-down technique. As a corollary, we conclude that a rational surface CP² 7CP² admits an exotic smooth structure.