can i update my core 2 duo

Luminary

Admirable
In order to be able to answer your question we'll need to know a bit more about your hardware.

Is your computer a laptop or desktop?
If your computer is a desktop, did you build it yourself or buy it pre-built?
If your computer is pre-built, what is the make/ model?

Also, are you asking if it will be possible to replace a failed CPU with an identical model (replace with another Core 2 Duo), or are you asking if you can upgrade to a newer CPU?