Please find all real solutions to the following equation:
(x^211*x+29)^(x^217*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}.

Posted by tomarken
on 20210406 11:10:02 