Final answer:
In the given context, 'dispel' means to drive away or eliminate rumors or false beliefs, suggesting that the couple's public behavior effectively clarified to the public that their marriage was not in trouble.
Step-by-step explanation:
The word dispel in this context means to alleviate or remove doubts, misbeliefs, or false rumors, essentially to clarify by proving them to be wrong. By breaking down the word, the prefix dis- means 'apart' or 'reverse', and the suffix -pel means 'drive' or 'push'. Considering these definitions, dispel can be understood as to 'drive away' or 'push apart' the rumors about the couple's marriage.
In this sentence, the behavior of the famous couple at parties and red-carpet events served to dispel rumors that their marriage was in trouble, suggesting that their actions made it clear to the public that such rumors were unfounded.