"Il existe des bananes roses."
Translation:There are pink bananas.
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It is indeed more formal.The only place where I've heard the formulation "there exists xyz" is in mathematical proofs. Alternative formulations (in order of formality):
"Pink bananas exist." "There is such a thing as pink bananas." "Pink bananas are a thing."
I don't know if Duo accepts these, but it should in my opinion.
If I wanted to stress the existence of such delights, I would be far more likely to say either "Pink bananas exist" or "There exist pink bananas" than "There are pink bananas". I can almost hear the exclamation mark after the first two sentences, but the last sentence suggests no more than "There are (some) pink bananas on the table. Would you like one?". Maybe it is because the existential "There are" always cries out for a locative in English, so you always want to finish it off with what looks like redundancy but isn't really (There are pink bananas there).
"Il existe des bananes roses." The clue is "des", which sounds like "day" and indicates the plural.