A system's application servers need to be patched. The requirements for maintenance work are as follows: System downtime is not allowed. The application server in use must be in the sane patch status.

A rolling update is a deployment strategy for continuous availability in production, but 'three staging environments' encompasses the broader, iterative testing and validation process required for all listed requirements.

Patching directly on production servers would likely cause downtime and performance issues, failing to meet the core requirements for the maintenance work.

Blue-green deployment is an excellent technique for achieving zero-downtime updates and quick rollbacks in production, but 'three staging environments' describes the full lifecycle environment setup that ensures comprehensive testing before that production deployment.

Employing three staging environments (e.g., Development, Staging, Production) allows for a structured and thorough validation process of patches at each stage. This methodology ensures patches are rigorously tested before reaching production, mitigating risks, maintaining performance, enabling pre-deployment testing, and facilitating rapid recovery or rollback strategies when transitioning to the live environment.