Final answer:
Competition is the conflict resolution approach that quickly resolves issues at the expense of potentially damaging relationships, making it efficient yet potentially harmful to collaboration.
Step-by-step explanation:
The approach to resolving conflicts that is most likely to result in quick solutions but often leads to relational conflicts is competition. Competition occurs when one party seeks to achieve their goals or interests at the expense of another party, often disregarding others' needs or concerns. This win-lose situation can resolve the issue quickly because one side is effectively overpowering the other, but it generally fosters negative feelings and may damage relationships in the long term.