Are "adult" and "adulterate" cognates?
Solution 1:
Here are relevant discussions from three authorities.
From John Ayto, Arcade Dictionary of Word Origins (1990):
adultery [14(th century)] Neither adultery nor the related adulterate have any connection with adult. Both come ultimately from the Latin verb adulterare 'debauch, corrupt' (which may have been based on Latin alter 'other,' with the notion of pollution from some extraneous source). By the regular processes of phonetic change, adulterare passed into Old French as avoutrer, and this was the form which first reached English, as avouter (used both verbally, 'commit adultery,' and nominally, 'adulterer') and as the nouns avoutery 'adultery,' and avouterer 'adulterer.' Almost from the first they coexisted in English beside adult- forms deriving either from Low French or directly from Latin, and during the 15th to 17th centuries these gradually ousted the avout- forms. Adulter, the equivalent of avouter, clung on until the end of the 18th century, but the noun was superseded in the end by adulterer and the verb by a new form, adulterate, directly based on the past participle of Latin adulterare, which continued to mean 'commit adultery' until the mid 19th century.
From Robert Hendrickson, The Facts on File Encyclopedia of Word and Phrase Origins (1997):
adultery. Contrary to popular opinion this word is not related to adult. It can be traced back to the Latin adulterare, "to pollute, to commit adultery," which also gives us the word adulterate. Interestingly, the English word adulterate once meant to commit adultery, Shakespeare using it in King John (1596): "She adulterates hourly with thine Uncle John."
From Merriam-Webster, Webster's Word Histories (1989):
adolescent The English adjectives adolescent, adult, and old, which designate stages of life, share a common Indo-European ancestor, whose meaning was 'to nourish' or 'to grow'. Alere, 'to nourish', and its derivative alescere, 'to grow', are Latin descendants of this Indo-European root. Latin adolescere, 'to grow up', is formed by the addition of the common Latin prefix ad-, meaning 'to' or 'at', to the verb alescere. The present participle of adolescere is adolescens, which gives us English adolescent; an adolescent person, then, is one who is growing up. A person who is an adult has grown up: Latin adultus is the past participle of adolescere.