Question-195413

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

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

$$x^y+y^x=8\Rightarrow x=y=2$$$$x+y=k^2\Rightarrow k^2=2+2=4\Rightarrow k=\pm 2$$$$k+1=\pm 2+1=3,-1$$

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

$$Yessirmyanswerisnotacomplete$$$$solution.$$

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

$$SeeanswerofmrWsirtothe$$$$\text{You can't use 'macro parameter character \#' in math mode}$$

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