I found this question on a math contest but I could not solve it and also could not find the solutions. If anyone could help: $$ 27^{3x^2+2y} + 27^{3y^2+2z}+27^{3z^2+2x} = 1$$ where $x,y,z \in \mathbb{R}$.
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2Hint: Modify this similar problem. If you're stuck, show your work. $\min (3x^2 + 2x) = - 1/3$, so the result follows. – Calvin Lin Oct 27 '20 at 14:52