If you purchased a physical copy, the activation key is printed on a plastic card (similar to a credit card) inside the box. Unlike many other software companies, Blackmagic does not store these keys in a "user account" on their website. If you lose this physical card, it is very difficult to recover the key.
If you have already purchased DaVinci Resolve Studio legally and cannot locate your key, you do not need a patch. Here is exactly where your authentic key is stored: where do i find my davinci resolve activation key patched
If your license came with hardware (like a Speed Editor or a camera), the key is usually on a card inside that hardware's packaging. How to Recover a Lost Key If you purchased a physical copy, the activation