Both of these verbs are used for asking about something or looking for information. The nouns for the request / investigation are enquiry and inquiry.
Technically, enquire is used for "ask" in general ("He enquired about prices for the products"), and inquire for a more formal investigation ("The police will make an inquiry into the alleged corruption.")
However, in American English it is now very common to use inquire for everything: "He inquired about prices for the products."
Mike Myers, Eddie Murphy and Cameron Diaz lend their voices to this outrageously funny comedy with dazzling computer animation. Its a fractured fairy tale about an ogre who falls in love with a princess. Its also a clever and sophisticated spoof of childrens stories and all things Disney.