I would use either 2"x 12" joists or add a 2" x 4" glued and nailed to the bottom of the 2"x 10". There will be some bounce otherwise, that would stiffen it up. 45' without any posts? That will be a huge beam. I have a 29' span, no posts and I used an 18" x 45 beam, nice and solid, no ctr posts. If you can find and afford a steel beam of the required size, I would try to get it and not use any support post- they are always in the way at some point, no matter where they are placed.