BMAD Posted October 5, 2017 Report Share Posted October 5, 2017 For 0<x<y find an integer solution for x^y = y^x Quote Link to comment Share on other sites More sharing options...
0 Molly Mae Posted October 6, 2017 Report Share Posted October 6, 2017 12 hours ago, BMAD said: For 0<x<y find an integer solution for x^y = y^x Pretty easy answer: x=2, y=4 Quote Link to comment Share on other sites More sharing options...
0 BMAD Posted October 9, 2017 Author Report Share Posted October 9, 2017 (edited) On 10/5/2017 at 10:56 PM, Molly Mae said: Hide contents Pretty easy answer: x=2, y=4 is there another? Edited October 9, 2017 by BMAD Quote Link to comment Share on other sites More sharing options...
0 Molly Mae Posted October 9, 2017 Report Share Posted October 9, 2017 (edited) 3 hours ago, BMAD said: is there another? Not integers for 0>x>y Edited October 9, 2017 by Molly Mae Quote Link to comment Share on other sites More sharing options...
0 Buddyboy3000 Posted October 9, 2017 Report Share Posted October 9, 2017 Spoiler Technically, there are an infinite amount of solutions for this equation. To find a solution, you can plug any value for the integer "a" to get a value for x and y. If "a" is any integer greater than 1, then the the solution is: x=a-1sqrt(a) y=a-1sqrt(a^a) Examples: a=1.5 x=2.25 y=3.375 2.25^3.375 = 3.375^2.25 = 15.43888... a=2 x=2 y=4 2^4 = 4^2 = 16 a=3 x=sqrt(3) y=sqrt(27) sqrt(3)^sqrt(27) = sqrt(27)^sqrt(3) = 17.36190... a=4 x=3sqrt(4) y=3sqrt(256) 3sqrt(4)^3sqrt(256) = 3sqrt(256)^3sqrt(4) = 18.80532... Quote Link to comment Share on other sites More sharing options...
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BMAD
For 0<x<y find an integer solution for
x^y = y^x
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