Question Number 167086 by mathlove last updated on 06/Mar/22
Commented by cortano1 last updated on 06/Mar/22
$$\:\mathrm{f}\left(\mathrm{x}\right)+\mathrm{f}\left(\mathrm{1}−\mathrm{x}\right)=\frac{\mathrm{x}^{\mathrm{2010}} }{\mathrm{x}^{\mathrm{2010}} +\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2010}} }+\frac{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2010}} }{\left(\mathrm{1}−\mathrm{x}\right)^{\mathrm{2010}} +\mathrm{x}^{\mathrm{2010}} }=\mathrm{1} \\ $$$$=\:\mathrm{1005} \\ $$