Question Number 190025 by Shrinava last updated on 26/Mar/23
$$\mathrm{If}\:\:\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{5}} \:+\:\mathrm{2x}^{\mathrm{2}} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{f}\left(\sqrt{\mathrm{2}}\:−\:\mathrm{1}\right)\:+\:\mathrm{f}\left(\mathrm{1}\:−\:\sqrt{\mathrm{2}}\right)\:+\:\mathrm{3} \\ $$
Answered by SEKRET last updated on 26/Mar/23
$$\:\:\:\sqrt{\mathrm{2}\:\:}\:−\mathrm{1}\:=\:\boldsymbol{\mathrm{a}}\:\:\:\:\:\:\:\:\mathrm{1}−\sqrt{\mathrm{2}}\:\:=\:−\boldsymbol{\mathrm{a}} \\ $$$$\:\:\mathrm{3}\boldsymbol{\mathrm{a}}^{\mathrm{5}} +\mathrm{2}\boldsymbol{\mathrm{a}}^{\mathrm{2}} \:−\:\mathrm{3}\boldsymbol{\mathrm{a}}^{\mathrm{5}} \:+\:\mathrm{2}\boldsymbol{\mathrm{a}}^{\mathrm{2}} \:+\mathrm{3}= \\ $$$$\:\:\mathrm{4}\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\mathrm{3}= \\ $$$$\mathrm{4}\left(\sqrt{\mathrm{2}}\:−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{3}= \\ $$$$\:\:\mathrm{4}\left(\mathrm{3}\:−\:\mathrm{2}\sqrt{\mathrm{2}}\:\right)+\mathrm{3}= \\ $$$$\:\:\mathrm{15}\:−\:\mathrm{8}\sqrt{\mathrm{2}} \\ $$
Commented by Shrinava last updated on 26/Mar/23
$$\mathrm{thank}\:\mathrm{you}\:\mathrm{professor} \\ $$