Verified answer

Since any number raised to the zeroth power is 1, and 1 raised to any power is 1,

x^2-9x+20 = (x-4)(x-5) = 0

x = 4 or x = 5

x^2-5x+5 = 1

=>x^2-5x+4 = (x-1)(x-4) = 0

x = 1 or x = 4

So, the combined solution is x = 1, 4, 5 (Edit)

x = 4.0619427978

Edit: This is the only real root for

(x²-5x+5)^(x²) -9x+20=1 or, as your equation can be rewritten:

[ (x²-5x+5)^(x)] [ (x²-5x+5)^(x) ] -9x+20-1 = 0

Solved by graphing and finding the zero point.

Of interest is when x = 2, y = 2 and when x = 3, y = -7

Very interesting graph. Where did you find this problem; does it have a practical application (string theory maybe?)

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