A simple equation, can Mathematica solve it?

*Subject*: [mg2610] A simple equation, can Mathematica solve it?*From*: jiri at pica.com.au (Jiri Vitesnik)*Date*: Mon, 27 Nov 1995 21:36:06 -0500*Approved*: usenet@wri.com*Distribution*: local*Newsgroups*: wri.mathgroup*Organization*: Wolfram Research, Inc.

2:00 PM 27/11/95 A simple equation, can Mathematica solve it? 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= er. 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 Jiri