This was a game of dancing. I managed to take my opponent's Queen, but at a cost. In the end, my Queen and his two Rooks were dancing around in an effort to advance Pawns. So busy with advancing Pawns that I missed the mating move the first time. In the end, though, I was able to mate using my Queen and a Pawn, with his Rooks blocking any escape.
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This game had several interesting situations, regarding two rooks versus a lone queen, though you had the advantage, for a while, of some extra pawns.
Two rooks usually seemed to me to be a big handful for a Queen to handle, if the guy with the Rooks used them together. I didn't see where he could win but in your opponent's shoes I would've gone for the draw -- or even the win if you messed up -- by trying to double those rooks on your second rank as quick as I could, following the tried and true chess adage that "two rooks on their seventh rank are like a couple of blind pigs." Or lining them up behind your Queen-side P's. BEHIND P's is where Rooks should be in the endgame.
Failing that, near the end, when you just had the one P coming down, you might've had trouble making any headway if he had just kept moving those two Rooks back and forth on their third rank, while keeping your K from coming out to help by always keeping one of the rooks on the KB file.