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Question-183974




Question Number 183974 by yaslm last updated on 01/Jan/23
Answered by MJS_new last updated on 01/Jan/23
x=y^3 +12y+7  y^3 +12y+(7−y)=0  use Cardano′s Formula to get  y=((((x−7)/2)−((√(x^2 −14x+305))/2)))^(1/3) +((((x−7)/2)+((√(x^2 −14x+305))/2)))^(1/3)
$${x}={y}^{\mathrm{3}} +\mathrm{12}{y}+\mathrm{7} \\ $$$${y}^{\mathrm{3}} +\mathrm{12}{y}+\left(\mathrm{7}−{y}\right)=\mathrm{0} \\ $$$$\mathrm{use}\:\mathrm{Cardano}'\mathrm{s}\:\mathrm{Formula}\:\mathrm{to}\:\mathrm{get} \\ $$$${y}=\sqrt[{\mathrm{3}}]{\frac{{x}−\mathrm{7}}{\mathrm{2}}−\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{14}{x}+\mathrm{305}}}{\mathrm{2}}}+\sqrt[{\mathrm{3}}]{\frac{{x}−\mathrm{7}}{\mathrm{2}}+\frac{\sqrt{{x}^{\mathrm{2}} −\mathrm{14}{x}+\mathrm{305}}}{\mathrm{2}}} \\ $$

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