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.
(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}.
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Posted by tomarken
on 2021-04-06 11:10:02 |
re: proposed solution - a couple more
