In addition to keeping the nobles and royal princes busy so that they would stay out of politics, what other reason could explain why Louis XIV invited them to the royal court?

Another reason why Louis XIV invited the nobles and royal princes to the royal court was to keep them under his watchful eye so that they do not plot anything against the throne, his throne.

Explanation:

King Louis XIV was the king of France after the death of Louis XIII. His interest in the Palace of Versailles led to the beginning of more extensions and renovations done to the place.

The reason for this renovation was to make the nobles and royal princes live within the court premises. This will render them unable to plot anything against the king. Moreover, the presence of the nobles and princes within his sight means that he can have more control over the government and have no opposition from them.

Thus, aside from the plot to keep the nobles and princes away from politics, Louis XIV made them stay in the royal court so that he will be able to keep an eye on all of them and ensure no plot schemes against him.

there is no photo, therefore i can not answer your question.