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Question Number 104973 by malwaan last updated on 25/Jul/20

$$2\sqrt{3}+\mathit{i}isacubicrootfor$$$$18\sqrt{3}+35\mathit{i}$$$$\mathit{f}\mathit{i}\mathit{n}\mathit{d}\mathit{t}\mathit{h}\mathit{e}\mathit{o}\mathit{t}\mathit{h}\mathit{e}\mathit{r}2\mathit{c}\mathit{u}\mathit{b}\mathit{i}\mathit{c}\mathit{r}\mathit{o}\mathit{o}\mathit{t}\mathit{s}$$

Commented by malwaan last updated on 25/Jul/20

شكرا جزيلا سيدي الفاضل واذا كان لديك طريقة او لوحة مفاتيح لكتابة المعادلات والنهايات والتكاملات وغيرها باللغة العربية فاتمنى تساعدني مع فائق احترامي محمد علوان اليمن

Answered by Rasheed.Sindhi last updated on 25/Jul/20

$$Letaisagivencuberootofx$$$$\left(say\right)$$$$\therefore x^3=a^3\Rightarrow x^3-a^3=0$$$$\Rightarrow (x-a)(x^2+ax+a^2)=0$$$$\Rightarrow x-a=0\vee x^2+ax+a^2=0$$$$x=a\left(given\right)\vee x=\frac{-a\pm \sqrt{a^2-4a^2}}{2}$$$$x=\frac{-a\pm ai\sqrt{3}}{2}=a\left(\frac{-1\pm i\sqrt{3}}{2}\right)$$$$x=a\omega ,a{\omega }^2$$$$a=2\sqrt{3}+\mathit{i}\to$$$$x=(2\sqrt{3}+\mathit{i})\omega ,(2\sqrt{3}+\mathit{i}){\omega }^2$$$$\left(Othertwocuberoots\right)$$

Commented by malwaan last updated on 25/Jul/20

$$wow$$$$howdoyouwriteinarabicsir?$$$$fromthisapporother?$$

Commented by Rasheed.Sindhi last updated on 25/Jul/20

Use the option 'plain text comment' to write with your arabic keyboard: ل^۲+۸ل+۲۲=۷ √(8)=2√(2)

Commented by Rasheed.Sindhi last updated on 25/Jul/20

لا ريب يا سيدي!

Commented by malwaan last updated on 25/Jul/20

$$thanksirRasheed$$$$andifwewanttheanswer$$$$withoutusing\omega and{\omega }^2$$$$x=(2\sqrt{3}+i)\left(\frac{-1+i\sqrt{3}}{2}\right)=\frac{-3\sqrt{3}+5i}{2}$$$$x=(2\sqrt{3}+i)\left(\frac{-1-i\sqrt{3}}{2}\right)=\frac{-\sqrt{3}-7i}{2}$$

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