ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ
The words ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ occur in a famous passage in the Apology in which Socrates explains why he will not abandon φιλοσοφία.
"Someone might say, 'Socrates, can you not go away from us and live quietly, without talking?' Now this is the hardest thing to make some of you believe. For if I say that such conduct would be disobedience to the god and therefore I cannot keep quiet, you will think I am jesting and will not believe me; and if again I say that to talk every day about virtue (ἀρετῆς) and the other things about which you hear me talking and examining myself and others is the greatest good to man, and that the unexamined life is not worth living [or: the unexamined life is not to be lived by man (ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ)], you will believe me still less. This is as I say, gentlemen, but it is not easy to convince you" (Apology 37e-38a).
What Socrates seemed to glimpse about human beings and "virtue" (ἀρετή) is the principal issue that occupies Plato and much of the subsequent ancient philosophical tradition.
What Plato has Socrates say shows the outline of what Plato thought Socrates glimpsed. Socrates implies, in his remarks, that some lives are better than others, that as human beings become adults they acquire mistaken beliefs about what is good and what is bad, that "examining" themselves and others by asking and trying to answer questions about "virtue" and related matters is necessary for them to rid themselves of these mistaken beliefs, and that this process is necessary for them to live a life that is best for a human being. This life, whatever it is, is "the good life."
Perseus Digital Library:
Henry George Liddell, Robert Scott, A Greek-English Lexicon:
ἀνεξέταστος, anexetastos, adjective, "not searched out,"
ἐξετάζω, exetazō, verb, "to examine well,"
ἀρετή, aretē, noun, "virtue"