An interesting equation

December 28th, 2004 ~ Posted in: General

Solve this equation: \left(x^2-3x+3\right)^2-3\left(x^2-3x+3\right) +3=x.

I already got the two `easy’ roots, but I haven’t been able to get the other two. Maybe I’ll have to resort to expanding the polynomial and using synthetic division, but considering the source of this problem, I think there is a more elegant solution than that.

Update: I couldn’t find such an elegant manner of finishing the problem, so I peeked at the solution, and found that they did use synthetic division! Moral being, don’t be afraid of a little grunt work…

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