Question Number 18827 by aplus last updated on 30/Jul/17
Commented by aplus last updated on 30/Jul/17
$$\mathrm{help}\:\mathrm{guys} \\ $$
Commented by mrW1 last updated on 30/Jul/17
$$\mathrm{no}\:\mathrm{solution} \\ $$
Commented by dioph last updated on 31/Jul/17
$$\mathrm{if}\:\mathrm{both}\:{x}\:\mathrm{and}\:{y}\:\mathrm{are}\:>\:\mathrm{1}: \\ $$$${x}^{{x}} \:>\:{x},\:{y}^{{y}} \:>\:{y}\:\Rightarrow\:{x}^{{x}} \:+\:{y}^{{y}} \:>\:{x}\:+\:{y} \\ $$$$\Rightarrow\:\mathrm{6}\:>\:\mathrm{35},\:\mathrm{absurd} \\ $$$$\mathrm{if}\:\mathrm{exactly}\:\mathrm{one}\:\mathrm{from}\:{x}\:\mathrm{or}\:{y}\:\mathrm{is}\:<\:\mathrm{1}, \\ $$$$\mathrm{say}\:{x}\:<\:\mathrm{1}: \\ $$$${x}\:+\:{y}\:=\:\mathrm{35}\:\Rightarrow\:{y}\:>\:\mathrm{34}\:\Rightarrow\:{y}^{{y}} \:>\:\mathrm{34}^{\mathrm{34}} \\ $$$$\Rightarrow\:{x}^{{x}} \:+\:{y}^{{y}} \:>\:\mathrm{6},\:\mathrm{absurd} \\ $$$$\mathrm{if}\:\mathrm{both}\:{x}\:\mathrm{and}\:{y}\:\mathrm{are}\:<\:\mathrm{1}: \\ $$$${x}\:+\:{y}\:<\:\mathrm{2}\:<\:\mathrm{35},\:\mathrm{absurd} \\ $$