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Qd3 is enough to win!!
I dont think so friends... after Qh5, if black plays Kf8, white has no other options than draw the match... if not, white will lose either Bishop or Knight, both are unprotected. Qd3, protects both, which is easy way to win keeping extra material as advantage.
1 Qh5, Kf8 2.dxe6, if black played Nxe6
exd6 if queen takes bishop qf7+ then ke8, and qxd7#
Looks like there are many solutions here.
1. Qh5+ is pretty simple. If 1... Kd8/e7, at the very least there's 2. Qh4+ grabbing the knight. If 1... Kf8 there's 2. Rb1 attacking the queen, and threatening mate if she moves. If 2... Qe7, at the very least there's 3. Rb8+ Kg7 4. Qg4+ followed by taking the rook.