Prove that the likelihood ratio test for hypotheses (9.5.7) is the two-sided t test that rejects H0

Question:

Prove that the likelihood ratio test for hypotheses (9.5.7) is the two-sided t test that rejects H0 if |U| ≥ c, where U is defined in Eq. (8.5.1). The argument is slightly simpler than, but very similar to, the one given in the text for the one-sided case.