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Question Number 195413 by Calculusboy last updated on 02/Aug/23

Commented by Rasheed.Sindhi last updated on 02/Aug/23

x^y +y^x =8⇒x=y=2 x+y=k^2 ⇒k^2 =2+2=4⇒k=±2 k+1=±2+1=3,−1

xy+yx=8⇒x=y=2x+y=k2⇒k2=2+2=4⇒k=±2k+1=±2+1=3,−1

Commented by TheHoneyCat last updated on 03/Aug/23

quite a lazy and un-rigorous proof by Rasheed Sindhi, (for instance x=y=2 is not the only solution, you also have (1,7)) but (assuming we are only looking for integer values of k), his final results is correct. And easy to verify. Hence I am promoting it to an answer, if anyone wants details, please ask.

Commented by Rasheed.Sindhi last updated on 03/Aug/23

Yes sir my answer is not a complete solution.

Yessirmyanswerisnotacompletesolution.

Commented by TheHoneyCat last updated on 03/Aug/23

Yes, no problem. I was just justifying "promoting it to answer" because I think its sufficient for anyone to find the details on their own, starting from what you wrote.

Commented by Rasheed.Sindhi last updated on 04/Aug/23

See answer of mr W sir to the Q#195511

SeeanswerofmrWsirtotheYou can't use 'macro parameter character #' in math mode

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