Question Number 119059 by qqqqqqqqq last updated on 21/Oct/20
Answered by MJS_new last updated on 21/Oct/20
$$\sqrt{{x}^{\mathrm{2}} +{x}^{\mathrm{2}} \left({x}+\mathrm{1}\right)^{\mathrm{2}} +\left({x}+\mathrm{1}\right)^{\mathrm{2}} }−{x}^{\mathrm{2}} = \\ $$$$=\sqrt{{x}^{\mathrm{4}} +\mathrm{2}{x}^{\mathrm{3}} +\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{1}}−{x}^{\mathrm{2}} = \\ $$$$=\sqrt{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }−{x}^{\mathrm{2}} = \\ $$$$={x}^{\mathrm{2}} +{x}+\mathrm{1}−{x}^{\mathrm{2}} ={x}+\mathrm{1} \\ $$$${x}=\mathrm{2003}\:\Rightarrow\:\mathrm{answer}\:\mathrm{is}\:\mathrm{2004} \\ $$