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A simple equation, can Mathematica solve it?

                 2:00 PM      27/11/95
 A simple equation, can Mathematica solve
I was recently given a competition problem to test Mathematica's equation=
 solving capabilities.

Solve[(x^2 - 5x + 5)^(x^2 - 9x + 20) =3D=3D 1,x]

An easy question to do with little knowledge, a pencil and a piece of pap=

Mathematica can be useful; but:
Solve makes no attempt even though I was told that some competing product=
s give the x=3D4 & x=3D5 solutions.
Graphing the function:
Plot[(x^2 - 5x + 5)^(x^2 - 9x + 20) - 1,{x,0.9,5}] will provide the third=
 solution of x=3D1. To get the right domain requires a little understandi=
ng and patience.
The final two solutions will come to light with:
Table[{x,x^2 - 5x + 5)^(x^2 - 9x + 20) - 1},{x,1,4,.1}]

Can Mathematica be used in a more elegant way to give the full solution?

Kind regards


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