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."
Atal Bihari Vajpayee was born into a middle class family in Gwalior. His father was Krishna Bihari Vajpayee, a school teacher and poet, and his mother was Krishna Devi.He attended the Saraswati Shishu Mandir and later went to Victoria College from where he graduated with distinction in Hindi, English and Sanskrit.
He enrolled at DAV College, Kanpur to complete his post graduation and earned his M.A. in Political science. He was a patriot at heart and participated in Indias struggle for freedom even as a student and edited several nationalist Hindi newspapers.