Question Number 161126 by geron last updated on 12/Dec/21
Commented by geron last updated on 12/Dec/21
$$\mathrm{79}\:? \\ $$
Commented by geron last updated on 12/Dec/21
$$\boldsymbol{{P}}\left({x}\right):\boldsymbol{{Q}}\left({x}\right)={f}\left({x}\right)+\boldsymbol{{k}},\:\boldsymbol{{k}}=? \\ $$
Answered by TheSupreme last updated on 12/Dec/21
$$\mathrm{79} \\ $$$$\left({x}^{\mathrm{2}} +\mathrm{2014}{x}+\mathrm{2015}\right)\left({x}^{\mathrm{2}} +\mathrm{2015}{x}+\mathrm{2016}\right)+\left({x}^{\mathrm{2}} +\mathrm{2013}{x}+\mathrm{2014}\right)\left({x}^{\mathrm{2}} +\mathrm{2017}{x}+\mathrm{2018}\right)+\mathrm{3}{x}+\mathrm{2}/\left({x}^{\mathrm{2}} +\mathrm{2016}{x}+\mathrm{2017}\right) \\ $$$$\left({P}\left({x}\right)−\mathrm{2}{x}−\mathrm{2}\right)\left({P}\left({x}\right)−{x}−\mathrm{1}\right)+\left({P}\left({x}\right)−\mathrm{3}{x}−\mathrm{3}\right)\left({P}\left({x}\right)+{x}+\mathrm{1}\right)+\mathrm{3}{x}+\mathrm{2} \\ $$$$\left(−\mathrm{2}{x}−\mathrm{2}\right)\left(−{x}−\mathrm{1}\right)+\left(−\mathrm{3}{x}−\mathrm{3}\right)\left({x}+\mathrm{1}\right)+\mathrm{3}{x}+\mathrm{2}= \\ $$$$=\mathrm{2}\left({x}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{3}\left({x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}= \\ $$$$=−{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}+\mathrm{3}{x}+\mathrm{2}=−{x}^{\mathrm{2}} +{x}+\mathrm{1}/\left({x}^{\mathrm{2}} +\mathrm{2016}{x}+\mathrm{2017}\right) \\ $$$$=\mathrm{2017}{x}+\mathrm{2018} \\ $$
Commented by Rasheed.Sindhi last updated on 13/Dec/21
$$\mathrm{Typo}\:\mathrm{sir}:\:{In}\:\mathrm{3}{rd}\:{line}\:{you}'{ve}\:{written} \\ $$$${P}\left({x}\right)\:{instead}\:{of}\:{Q}\left({x}\right). \\ $$