Final answer:
Hyaluronic acid injection is the approved treatment for OA knee pain, delivering relief for up to 12 weeks, unlike fentanyl, methadone, or buprenorphine-naloxone which are opioids used for severe pain and carry an addiction risk.
Step-by-step explanation:
The medication that is approved for osteoarthritis (OA) knee pain and is administered into the knee joint providing up to 12 weeks of pain relief is Hyaluronic acid injection. This treatment is quite different from the opioid medications like fentanyl, methadone, or buprenorphine-naloxone, which are powerful pain relievers with a high risk of addiction and are generally reserved for severe pain that has not responded to other medications. Hyaluronic acid injections are often used in the treatment of knee OA when other non-surgical treatments, such as over-the-counter medication like acetaminophen and non-steroidal anti-inflammatory drugs (NSAIDs), do not adequately alleviate the pain.