This… feels like one of those “99% of people can’t do this basic math trick” memes. I mean, yeah, the puzzles are actually cool, but it feels strange to see such posts on a news website.
I solved it, to my own surprise, by considering a more general problem. I wanted to get an interval for the solution, so I replaced 3 with y. Now for y=5, the solution is obvious. x(y) is a increasing function and its minimum is... oh!
Not sure why this is supposed to be hard. Apollonius's theorem works as it's intended to here.<p>AB^2+AC^2=2AD^2+2BD^2<p><a href="https://www.wolframalpha.com/input?i=5%5E2%2B3%5E2%3D2x%5E2%2B2*4%5E2" rel="nofollow">https://www.wolframalpha.com/input?i=5%5E2%2B3%5E2%3D2x%5E2%...</a>