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Question Number 111008 by Khanacademy last updated on 01/Sep/20

$$\frac{\sqrt{\mathit{x}+1}}{\mathit{y}+2}+\frac{\sqrt{\mathit{y}+2}}{\mathit{x}+1}=1=>\mathit{x}=?$$

Commented byRasheed.Sindhi last updated on 01/Sep/20

$$xintermsofy?$$

Commented byKhanacademy last updated on 01/Sep/20

$$???????$$

Commented byHer_Majesty last updated on 01/Sep/20

$$complicated...$$ $$\frac{a}{b^2}+\frac{b}{a^2}=1$$ $$a^3-a^2{b}^2+b^3=0$$ $$a=t+\frac{b^2}{3}$$ $$t^3-\frac{b^4}{3}t-\frac{b^3(2b^3-27)}{27}=0$$ $$wecansolvethisfort$$ $$D=\frac{b^6}{4}-\frac{b^9}{27}$$ $$weneed{Cardano}^{\prime }sortheTrigonometric$$ $$solution$$ $$dependingonthedesireddomain:$$ $$\mathbb{R}:x>-1\wedge y>-2\Rightarrow a>0\wedge b>0$$ $$\mathbb{C}:x\ne -1\wedge y\ne -2\Rightarrow a\ne 0\wedge b\ne 0$$

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