Truck Idle low on 2005 Chevrolet Trailblazer

After I replaced the battery in the truck, when I run the AC, It idles low and sometimes shuts off. What would cause this? The replace ran a diag. and said that the #3 fuel injector has failed. They checked the compressor, sparks plug, etc. and all is well. . .

Asked by for the 2005 Chevrolet Trailblazer