Inquire and enquire differ by only a single letter, and they both mean, roughly, "ask". How should you choose which one to use?
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The Macquarie Dictionary suggests inquire as the dominant form (enquire directs readers to inquire), but also offers this usage note:
[In the case of] enquire and inquire, the forms are interchangeable. Some organisations, such as newspapers, tend to standardise on the in- form, but there are also those who make a distinction between, for example, an official inquiry and an informal enquiry.
Inquire appears more common in British English (and hence in written Australian English), while enquire is more common in American English. As the Macquarie notes, inquire is often said to refer to a more formal kind of investigation, and inquiry is usually the form used in Australia for government-instigated activities such as the the Fitzgerald Inquiry. In spoken English it isn't always clear which version you've heard, which can lead to confusion over spelling, though not usually over meaning.
As with many thorny language matters, consistency is the best approach: pick a single form and stick to it. If in doubt, we favour inquire and inquiry; that way, you won't mistakenly refer to a non-existent event such as the Fitzgerald Enquiry. Accuracy matters.
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