John and Yoko at the Grammy Awards
March 1, 1975

John and Yoko's first public appearance together after their reconciliation was at the  Grammy Awards in Los Angeles on March 1, 1975.

Anthony Fawcett quotes John in his book, "John Lennon: One Day At A Time" -

JOHN:
"I was glad it was so big, and it was quick, so we got maximum effect and it sort of said it without having to go through a big routine - it just sort of went in all the right papers and magazines, and there we were, and that's it.  There's nothing else to say - ha! ha! It's all over!  So it's good that I hadn't been seen around before that.

"At one time I was sort of on practically every TV show all the time and in every newspaper going on about immigration, and people got bored stiff, including me. Then the next bout was being drunk in Los Angeles, so I thought I better keep out of the way a bit...I was going to do the Grammys anyway, because I thought it was about time they saw I was not abnormal and drunk all the time, that I could speak, so I thought it would be a good opportunity to kill two birds with one stone - a) show that sometimes I'm sober, and b) that I was back with my wife and that everything, as far as I was concerned, was back to normal...

"We knew we were going to get back together one day, but it could've been ten years - it was fate, so we knew we'd get back together one way or another, but we'd no idea when."

John Lennon In His Own Words, Compiled by Miles:

"It's not a matter of who broke it up. It broke up. And why did we end up back together?  We got back together because we love each other. The separation didn't work out. That's it. It didn't work out. And the reaction to the breakup was all that madness. I was like a chicken without a head."