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If-f-x-3x-5-2x-2-Find-f-2-1-f-1-2-3-




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

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