If these are actual "Trojans", then a user of this Mac may have made some bad decisions regarding downloads and installations of software. However, you haven't been in anyway specific about the particular Trojans that were found.
I would not put it past a third party anti-malware application to "find" innocuous code, or even code that is only relevant to a Windows PC, and announce it has found some earth shattering monster Trojan in order to validate the existence of the product, and hence your desire to purchase updates and upgrades. However, I can't make this statement apply to your case without knowing what "Trojans" were actually found.
Bottom line.... Bit Defender is not needed, unless a user is habitually lax in installation decisions, or in some cases the user wishes an extra security blanket of protection for his underprotected networked Windows systems. Otherwise, Bit Defender is just another app taking up space, burning CPU cycles, and possibly costing you money to maintain.
Mountain Lion itself is reasonably secure in a reasonably cautious and sytem familiar user's hands. No other software is needed. If still there is a concern, opt for those that Apple has reviewed and passed in their App Store, such as ClamXav. I see that Bit Defender Scanner is the app store, but it would appear to be a markedly reduced feature set from an actual full time attendant type app. As such, it does not remain resident, and would be fine to keep around.
If your Mac's performance is slower than expected, the last thing you should do is download some app claiming the ability to improve it. I know of no such program that is capable of achieving any performance improvement whatsoever on a Mac - in fact, most will do the opposite. The remainder will do nothing.
Slow performance is usually due to insufficient memory, insufficient disk space, or poorly implemented third party system modifications. In some cases it is due to hardware failure, including disk corruption. Some programs will burden your Mac's resources more than others, and as apps evolve to become more demanding you will eventually want a newer Mac if you want to use those more demanding apps.
Determining the cause of your slowdowns will require more information. Start by reading this guide:
If you need more recommendations here are some to consider:
General purpose Mac troubleshooting guide: Isolating issues in Mac OS X
Creating a temporary account to isolate user-specific problems: Isolating an issue by using another user account
Identifying resource hogs and other tips: Runaway applications can shorten battery runtime
To identify potential hardware problems: Apple Hardware Test
To resolve startup issues and perform disk maintenance, use Disk Utility.
Safe Mode or "Safe Boot" is a troubleshooting mode that bypasses all third party system extensions and loads only required system components.
Read about it: Starting up in Safe ModeMacBooks iMacs iPads AirPorts, OS X Mountain Lion, 27 years Apple!
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