Question Number 11661 by @ANTARES_VY last updated on 29/Mar/17
$$\mathrm{8}\boldsymbol{\mathrm{x}}^{\mathrm{3}} −\mathrm{6}\boldsymbol{\mathrm{x}}+\mathrm{1}=\mathrm{0}. \\ $$$$\boldsymbol{\mathrm{Solves}}…\:\:\boldsymbol{\mathrm{equation}} \\ $$$$\boldsymbol{\mathrm{x}}_{\mathrm{1}} =?\:\:\:\:\:\boldsymbol{\mathrm{x}}_{\mathrm{2}} =? \\ $$
Answered by Joel576 last updated on 29/Mar/17
$$\mathrm{8}{x}^{\mathrm{3}} \:−\:\mathrm{6}{x}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$$$\Rightarrow\:\left({x}\:+\:\mathrm{1}\right)\left(\mathrm{8}{x}^{\mathrm{2}} \:−\:\mathrm{8}{x}\:+\:\mathrm{2}\right)\:=\:\mathrm{0} \\ $$$$\Rightarrow\:{x}\:+\:\mathrm{1}\:=\:\mathrm{0}\:\:\:\:\:\mathrm{or}\:\:\:\:\mathrm{8}{x}^{\mathrm{2}} \:−\:\mathrm{8}{x}\:+\:\mathrm{2}\:=\:\mathrm{0}\:\:\: \\ $$$$\bullet\:{x}\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$$$\:\:\:\:{x}\:=\:−\mathrm{1} \\ $$$$\bullet\:\mathrm{2}\left(\mathrm{4}{x}^{\mathrm{2}} \:−\:\mathrm{4}{x}\:+\:\mathrm{1}\right)\:=\:\mathrm{0} \\ $$$$\:\:\:\left(\mathrm{2}{x}\:−\:\mathrm{1}\right)^{\mathrm{2}} \:=\:\mathrm{0} \\ $$$$\:\:\:\:{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by @ANTARES_VY last updated on 29/Mar/17
$$????? \\ $$
Commented by @ANTARES_VY last updated on 29/Mar/17
$$????? \\ $$
Commented by @ANTARES_VY last updated on 29/Mar/17
$$????? \\ $$
Commented by Joel576 last updated on 30/Mar/17
$$\mathrm{Hmm},\:\mathrm{before}\:\mathrm{that}\:\mathrm{you}\:\mathrm{wrote} \\ $$$$\mathrm{8}{x}^{\mathrm{3}} \:−\:\mathrm{6}{x}\:+\:\mathrm{2}\:=\:\mathrm{0} \\ $$