The PHB says that when leveling up, instead of actually rolling for hit points you can take the "average" (actually average+.5) of your HD. Now, I've always played that you then add your CON bonus either way, and I'm not the only one; it says so explicitly in How do you calculate your character's Maximum Hit Points in D&D 5th Edition? and would certainly have come up in the answers to Why would I ever choose rolling hit points? if it were otherwise.
But one of my players just pointed out that the exact wording on PHB p. 16 is:
Each time you gain a level, you gain 1 additional Hit Die. Roll that Hit Die, add your Constitution modifier to the roll, and add the total to your hit point maximum. Alternatively, use the fixed value shown in your class entry, which is the average result of the die roll (rounded up).
The fact that "Alternatively..." is in a separate sentence implies that if you don't roll, you don't get the benefit of your CON bonus, which certainly changes the equation. Where does it say explicitly that you add your CON bonus either way?