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Question-199659




Question Number 199659 by cherokeesay last updated on 06/Nov/23
Answered by Frix last updated on 07/Nov/23
If we stay in R ⇒ ((−r))^(1/3) =−(r)^(1/3)   Obvious solutions  x=−1∨x=0  Not so obvious solutions  x=(1/2)±((√5)/2)  The method is: don′t believe what you see,  try nice numbers first.
$$\mathrm{If}\:\mathrm{we}\:\mathrm{stay}\:\mathrm{in}\:\mathbb{R}\:\Rightarrow\:\sqrt[{\mathrm{3}}]{−{r}}=−\sqrt[{\mathrm{3}}]{{r}} \\ $$$$\mathrm{Obvious}\:\mathrm{solutions} \\ $$$${x}=−\mathrm{1}\vee{x}=\mathrm{0} \\ $$$$\mathrm{Not}\:\mathrm{so}\:\mathrm{obvious}\:\mathrm{solutions} \\ $$$${x}=\frac{\mathrm{1}}{\mathrm{2}}\pm\frac{\sqrt{\mathrm{5}}}{\mathrm{2}} \\ $$$$\mathrm{The}\:\mathrm{method}\:\mathrm{is}:\:\mathrm{don}'\mathrm{t}\:\mathrm{believe}\:\mathrm{what}\:\mathrm{you}\:\mathrm{see}, \\ $$$$\mathrm{try}\:\mathrm{nice}\:\mathrm{numbers}\:\mathrm{first}. \\ $$

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