P.S. I mistyped it's "Black to move". I'm just too lazy to correct

 

Some of those tactic trainers that don't lead to check mate are a mystery to me

you must land a check to mate in two.. otherwise white can blow it's queen to make it a mate in 3 :P.

technicalities :P. 

I think Qg3 works fine.

It's for showing how to sacrifice Queen and your tactics trainer gave that puzzle to teach Q sacrifice...

I dislike such trainers. By having only one "correct" line when two or more are equally valid, and by focusing on massive sacrifices that are uncommon in game situations, the trainer encourages a separate mindset from actual games. With puzzles and trainers I always look for the most sensible way to sacrifice my queen, something that isn't wise in a game! Maybe trainers work for other people though.

Does it really matter if it's mate in three or two??? I won't care in real game! And for sure I would prefer not to sacrifice my queen...

 

Thanks for comments, everybody.