Question Number 12580 by @ANTARES_VY last updated on 26/Apr/17
$$\boldsymbol{\mathrm{Find}}\:\:\boldsymbol{\mathrm{the}}\:\:\boldsymbol{\mathrm{smaillest}}\:\:\boldsymbol{\mathrm{value}}\:\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{sum}} \\ $$$$\boldsymbol{\mathrm{x}}\left(\boldsymbol{\mathrm{x}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{2}\right)\left(\boldsymbol{\mathrm{x}}+\mathrm{3}\right). \\ $$
Answered by ajfour last updated on 26/Apr/17
$$\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{2}\right) \\ $$$$=\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)^{\mathrm{2}} +\mathrm{2}\left({x}^{\mathrm{2}} +\mathrm{3}{x}\right)+\mathrm{1}−\mathrm{1} \\ $$$$=\left({x}^{\mathrm{2}} +\mathrm{3}{x}+\mathrm{1}\right)^{\mathrm{2}} −\mathrm{1} \\ $$$${so}\:{its}\:{smallest}\:{value}\:{is}\:−\mathrm{1}\:. \\ $$
Commented by @ANTARES_VY last updated on 26/Apr/17
$$\mathrm{6}\boldsymbol{\mathrm{x}}^{\mathrm{3}} \:????? \\ $$
Commented by ajfour last updated on 26/Apr/17
$${what}'{s}\:{wrong}??? \\ $$