Determine the sum of all real numbers $x$ satisfying
\[(x^2-4x+2)^{x^2-5x+2} = 1.\]
Question:
Determine the sum of all real numbers $x$ satisfying
\[(x^2-4x+2)^{x^2-5x+2} = 1.\]
Answer:
Let's think step by step.

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Determine the sum of all real numbers $x$ satisfying
\[(x^2-4x+2)^{x^2-5x+2} = 1.\]
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