Powerful quadratics

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1. Find all real solutions of the equation \[{\large (x^2 - 7x + 11)^{(x^2 - 11x + 30)} = 1}.\]

If you were told that two numbers satisfied \[a^b=1,\] could you write down the possible numbers that \(a\) and \(b\) could be?

Can you apply the same logic to this question?

You might have to think hard to find all the solutions to the given equation. There are more than three solutions…