Question Number 186750 by pascal889 last updated on 09/Feb/23
Answered by Frix last updated on 09/Feb/23
$$\frac{\mathrm{1}+\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{4}} +\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{4}} }{\mathrm{1}+\left({x}−\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} +\left({x}+\frac{\mathrm{1}}{\mathrm{2}}\right)^{\mathrm{2}} }=\frac{\mathrm{2}{x}^{\mathrm{4}} +\mathrm{3}{x}^{\mathrm{2}} +\frac{\mathrm{9}}{\mathrm{8}}}{\mathrm{2}{x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{2}}}= \\ $$$$=\frac{\left({x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}\right)^{\mathrm{2}} }{\left({x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}}\right)}={x}^{\mathrm{2}} +\frac{\mathrm{3}}{\mathrm{4}} \\ $$$${x}=\mathrm{2009}.\mathrm{5}\:\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{4038091} \\ $$