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Heat pumps can't take the cold? Nordics debunk the myth
(techxplore.com)
This is a most excellent place for technology news and articles.
That is absolutely bonkers. I put one in myself for my one room garage that I converted to a place to hang. Cost 720$ after tax for a Pioneer mini split. It's entering its third year in use and I love it. That being said, I wouldn't be so risky as to put my own in when its task was heating or cooling my home. Just my garage is my problem, the rest is my family, and so I paid. But I got a whole home solution, two floors, Carrier units, for about $15k.
I believe what you're looking for is out there and not ridiculous price.