Absolutely. But on max? Maybe just barely. There's a HUGE difference in the hardware needed to run BF3 on maxed/ultra settings compared to high settings.
To run BF3 smoothly on high settings at 1920x1080, a Radeon HD 6870 will do- and average over 50fps. It would get approximately 60fps at 1600x900. http://www.tomshardware.com/reviews/batt... But for MAX settings at 1920x1080, you need at least a Radeon HD 6970 or GeForce GTX 570.
Technically, the Radeon HD 6950 or GeForce GTX 560 Ti would do (and your dual 5770's are roughly equivalent to that), but cards of that level only hit the mid-40's on fps. http://www.anandtech.com/show/5476/amd-r... So your current build is great for high settings, ultra is iffy. Your cheapest path to ultra would probably be a pair of Radeon HD 6850s in Crossfire, which would only cost maybe $50 more total (about $25 more per card).
However, that would require a stronger psu, like a 650W Corsair, XFX, or Antec.. the 700W Silverstone is also nice around that price. http://www.techpowerup.com/reviews/ATI/R... http://www.guru3d.com/article/radeon-hd-6850-6870-crossfirex-review/12.
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