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Why can't one cook for the second day of Yom Tov on the first day? Why won't something along the lines of Eiruv Tavshilin help in this case as well?
The format of a 2-day Yom Tov is a s'feika d'yoma. If Thursday is the Yom Tov, I cannot cook for Friday which is Chol (Rosh Hashana isn't exactly because of the same reason, but the same answer would apply).