Answer
In the Name of Allah, Most Gracious, Most Merciful.
All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.
In this fatwa:
One group of scholars affirms that the Prophet used to fast and may have skipped sometimes because of health challenges or other reasons. Regardless of whether the Prophet fasted or not, one may still do it.
Responding to your question, Sheikh Ahmad Kutty, a senior lecturer and an Islamic scholar at the Islamic Institute of Toronto, Ontario, Canada, states:
Whether the Prophet (peace be upon him) fasted the 9 days of Dhul-Hijjah is a controversial issue. We find two conflicting reports on this. One report from Aishah (may Allah be pleased with her) states, “I never saw the Prophet (peace be upon him) fasting any of the ten days (i.e., Dhul-Hijjah).” (Muslim)
However, there is another report attributed to one of the wives of the Prophet (without specifying the name) stating that the Prophet (peace be upon him) used to fast the nine days of Dhul-Hijjah, the 10th of Muharram, three days of every month and Mondays and Thursdays.” (Abu Dawud)
Some scholars of the hadith consider the latter report weak, while others deem it sound.
However, some traditions consider extolling the merits of good deeds performed in the first ten days of Dhul-Hijjah. Imam al-Bukhari reports on the authority of Ibn Abbas that the Prophet (peace be on him) said, “There are no days that good deeds are better than those done in the ten-day of Dhul-Hijjah).”
There is no reason to exclude fasting from the definition of good deeds.
Now, scholars are divided because of the contradictory reports mentioned above on whether the Prophet (peace be upon him) used to fast the first nine days of Dhul-Hijjah. One group affirms that he used to fast and may have skipped sometimes because of health challenges or other reasons. Since we know that the Prophet (peace be upon him ) would be the first to act upon the orders or recommendations he offers others, we must say that he will pay attention to fasting these days.
However, another group of scholars prefers to go by the tradition of Aishah (may Allah be pleased with her).
Having said this, I want to point out that regardless of whether the Prophet fasted or not, one may still do it. The Prophet may have skipped them for valid reasons. He is for sure the closest to Allah and more pious than us.
Almighty Allah knows best.