Powerful Problem (hint)

A few weeks ago I posted this “powerful” problem:

Solve \left(x^2-5x+5\right)^{\left(x^2-9x+20\right)}=1

Now, allow me to give you a major hint. Consider the simpler equation

a^b=1

What are the possible values of a and b? Here are the possible combinations:

    • a=1 and b is anything
    • b=0 and a is any nonzero number

And here’s the tricky one that most people forget:

    • a=-1 and b is even

You now have enough information to solve the original equation. I think you’ll be delighted with the solution!

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