# 8x-3-6x-1-0-Solves-equation-x-1-x-2-

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
$$\mathrm{Hmm},\:\mathrm{before}\:\mathrm{that}\:\mathrm{you}\:\mathrm{wrote} \\$$$$\mathrm{8}{x}^{\mathrm{3}} \:−\:\mathrm{6}{x}\:+\:\mathrm{2}\:=\:\mathrm{0} \\$$