Germany | Can you solve this ? | A Nice Math Olympiad Problem

[@antosandras]

Near the end, instead of (a+b)^4, it is much quicker to square equation (4), leading to a^4+b^4+2a^2b^2 = 4, i.e., a^4+b^4 = 4-2/4 = 7/2.

[@ratzou2]

Nice resolution, Worth mentioning you can figure out what a and b are definitively the moment you know a+b=1 and ab=-1/2, you just plug that into the quadratic formula and figure out that a and b are interchangibly (1-sqrt(3))/2 and (1+sqrt(3))/2. Although more practical and general, I do prefer the elegant solution proposed in the video to that one.

[@enjoymath2024]

Thanks so much for your thoughtful comment! You're absolutely right. I love that you shared that approach-it's a clear and efficient way to solve for a and b directly. I'm glad you enjoyed the alternate solution in the video, too! I think exploring different methods can really deepen our understanding. Thanks again for adding to the discussion!