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Practical English Usage - M Swan - Oxford U Press
"In British English, short question and negative forms of have are possible, though these are often formal. They are not used in American English.
Have you an appointment? (formal GB only)
Birmingham has not the charm of York or Edinburgh. (formal GB)
There is one idiomatic expression that uses this syntax in AmE: I've no idea. It is a dismissive statement indicating that the speaker has no interest in what is being discussed. It's meant to be less than helpful.
That example was well put but I don't think it is accurate. If you put it into another way it would be "You've no idea" instead of what is asked: "Have you no idea." This is incorrect.
I'm pretty sure that you won't find anyone who says stuff like that unless they're pretending to be smart, but the common expression is "Have you got an appointment" & "I have got no idea" I'm still not sure if 'got' is actually a proper word, but it is considered the proper spoken grammar anyway.
Oxford Learner's Dictionary:
"Have no idea, not have the faintest idea (informal) used to emphasize that you do not know something."
‘What's she talking about?’ ‘I've no idea.’
He hasn't the faintest idea how to manage people.
The use of "no" plus a noun is associated with emphatic speech.
The same goes for "You have a good book?" I have found myself phrasing questions in English using the Portuguese structure eg "We have a meeting today?", which although correct, is not the most natural way to ask the question. I think Duolingo may mark these alternatives incorrect to encourage a more natural response and discourage the habit of word for word translations.