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## Homework Statement

Let F be a field, and suppose that alpha is algebraic over F. Prove that if [F(alpha):F] is odd, then F(a^2)=F(a). {For those unfamiliar with notation [] denotes degree of extension and F(alpha) means F adjoined with alpha.)

## The Attempt at a Solution

Since [F(alpha):F] is odd the basis of F(alpha) consists of an odd number of elements. We also know that b in F(alpha) has the form c_0+c_1alpha+c_2alpha^2+...+c_n-1alpha^(n-1). I really have no idea how to proceed from here. Help would be much appreciated. Thanks.