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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.

See The Solution Submitted by Larry    
Rating: 3.0000 (1 votes)

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Solution re: proposed solution - a couple more Comment 3 of 3 |
(In reply to proposed solution by Charlie)

Either 

x^2 - 11x + 29 = 1
x^2 - 11x + 28 = 0
(x - 4)(x - 7) = 0
x = 4, 7

or 

x^2 - 17x + 72 = 0
(x - 8)(x - 9) = 0
x = 8, 9

OR

x^2 - 11x + 29 = -1 and (x^2 - 17x + 72) is even.
x^2 - 11x + 30 = 0
(x - 5)(x - 6) = 0
x = 5, 6

Either of these roots would make the exponent an even integer, so they are also solutions.  

So the expanded solution set is {4, 5, 6, 7, 8, 9}.







  Posted by tomarken on 2021-04-06 11:10:02
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