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Please find all real solutions to the following equation:

(x^2-11*x+29)^(x^2-17*x+72) = 1

Adapted from a problem by Presh Talwalkar.

 Submitted by Larry Rating: 3.0000 (1 votes) Solution: (Hide) I know of six solutions: {4,5,6,7,8,9} Consider this equation as base^exponent = 1 The exponent is (x-8)(x-9), so two solutions are 8 and 9, because anything (except zero) to the zero power is 1. The base can be written as (x-4)(x-7)+1 and therefore solutions 4 and 7 make the base equal to 1. One to any power equals 1. The base can also be written as (x-5)(x-6)-1 and therefore solutions 4 and 7 make the base equal to -1 and in each of these cases the exponent will be an even number. And -1 to an even power equals 1.

 Subject Author Date re: proposed solution - a couple more tomarken 2021-04-06 11:10:02 More solutions Steve Herman 2021-04-06 11:09:11 proposed solution Charlie 2021-04-06 10:59:00

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