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quadratic ^ quadratic (Posted on 2021-04-06) Difficulty: 3 of 5
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.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionre: proposed solution - a couple moretomarken2021-04-06 11:10:02
SolutionMore solutionsSteve Herman2021-04-06 11:09:11
Solutionproposed solutionCharlie2021-04-06 10:59:00
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