Let  be a finite extension F of odd degree(greater than 1). Show that 

Given:
- \( F(\alpha) \) is a finite extension of \( F \) of odd degree.
- \( \alpha \) is an element of \( F(\alpha) \).

To show that \( F(\alpha^2) = F(\alpha) \), we need to prove two inclusions:

1. \( F(\alpha^2) \subseteq F(\alpha) \): This inclusion is straightforward because \( \alpha \) is ___ __________ ___ _________ ___ _____ ___.
__________ _____ _________ ____ _________ _________ _____ _____ __________ _____ ________ ___.
____ _________ ___ ____ _________ _______ _________ _____ _______ ___ _______.
_________ ________ ______ ________ ___ ______ ________ ________ ____ ___ _________.
___ _________ ___ _________ __________ ________ ______ _______ ________ ______ _____ ___.
__________ _______ ______ ___ ___ _________ __________ ___ _____ _________ _________ ___.
____ _____ ________ ________ _____.
______ ____ ____ _____ ___ __________ __________ ________ _____ _______ ____.
_______ __________ ______ _________ _________ _____ ________ ___ __________ _______.
____ _______ _____ ______ _______ ______ ______ ________.
______ _____ _______ _____ _____ ___ _____ _______ _______ _________.
_________ ________ _________ _____ ____.
__________ ___ ___ ___ _____.
___ _____ _________ __________ ____ _____ _____ ______ ____ _______.
______ _________ ______ ______ ______ _____.
________ _________ _______ __________ ____ __________ _______ _________ __________ _____ ______ _______.
________ _____ ___ _____ ______ _____ ________ ___ _________ ______.
______ _________ _______ ____ _____ _________ _____ _________ _________ _______.
_______ ____ ___ _____ ______.
__________ _______ _____ ___.
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