An Interesting Algebra Equation | AIME 2014

[moeberry]

Hands down the best algebraic equation on YouTube! Turning a rational equation to a sectic polynomial with no complex solutions! And using symmetry multiple times through out the problem as well as using Intuition for the first 2 zeros found!

[lalitmarwaha]

When i saw this one i knew i was solving this one
This is one of those trick question
That you get the habit of
Like in a quartic equation you know by experience you have to make pairs
Great and enjoyable problem

[hilbertonfields]

these always trip me up, I often focus at the wrong stuff

[Deathranger]

Hey, this is one of the few problems I’ve seen here that’s I actually saw when it was used on AIME. I definitely didn’t solve it at the time, but I remember it for sure. Super fun problem, thanks for the video. :)

[math]

very well done, thanks for sharing the solution to this interesting algebra equation