Question Number 201796 by ajfour last updated on 12/Dec/23
$${x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{2}} −\mathrm{30}{x}+\mathrm{104}=\mathrm{0} \\ $$$${for}\:{x}\in\mathbb{R}\:\:\:\:\:{x}=\mathrm{2},\:\mathrm{4} \\ $$$${I}\:{want}\:{to}\:{know}\:{the}\:{best}\:{way}\:{to} \\ $$$${arrive}\:{at}\:{these}\:{answers}\:\left({without}\right. \\ $$$$\left.{guessing}\right).\:{I}\:{found}\:{one}\:{new}\:{way}. \\ $$$$\:{Shall}\:{post}\:{later}. \\ $$
Commented by Frix last updated on 12/Dec/23
$$\mathrm{Usually}\:\mathrm{it}'\mathrm{s}\:\mathrm{the}\:\mathrm{shortest}\:\mathrm{way}\:\mathrm{to}\:``\mathrm{guess}'' \\ $$$$\mathrm{trying}\:\mathrm{the}\:\pm\mathrm{factors}\:\mathrm{of}\:\mathrm{the}\:\mathrm{constant} \\ $$$$\mathrm{104}=\mathrm{2}^{\mathrm{3}} \mathrm{13} \\ $$$$\mathrm{This}\:\mathrm{doesn}'\mathrm{t}\:\mathrm{work}\:\mathrm{in}\:\mathrm{the}\:\mathrm{following}\:\mathrm{case}: \\ $$$${x}^{\mathrm{4}} −\mathrm{16}{x}^{\mathrm{2}} −\mathrm{36}{x}+\mathrm{91}=\mathrm{0} \\ $$$$\mathrm{I}'\mathrm{m}\:\mathrm{looking}\:\mathrm{forward}\:\mathrm{to}\:\mathrm{see}\:\mathrm{your}\:\mathrm{solution}. \\ $$
Commented by Calculusboy last updated on 15/Dec/23
$$\boldsymbol{{we}}\:\boldsymbol{{can}}\:{st}\boldsymbol{{ill}}\:\boldsymbol{{use}}\:\boldsymbol{{another}}\:\boldsymbol{{way}} \\ $$