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quadratic ^ quadratic (Posted on 2021-04-06)

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: 4.0000 (2 votes)

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proposed solution

| Comment 1 of 5

Either

x^2-11*x+29 = 1

x^2-17*x+72 = 0

first case:

x^2 - 11x + 28 = 0

x = (11 +/- sqrt(121 - 112))/2 = (11 +/- 3) = 4 or 7

second case:

x = (17 +/- sqrt(289 - 288))/2 = 8 or 9

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

Posted by Charlie on 2021-04-06 10:59:00

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