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Question Number 92831 by unknown last updated on 09/May/20

Commented by unknown last updated on 09/May/20

$$\mathrm{Solve}\mathrm{the}\mathrm{equation}(p,q,r)\mathrm{if}\mathrm{the}\mathrm{solution}\mathrm{are}\mathrm{real}\mathrm{number}$$

Commented by unknown last updated on 09/May/20

$$\mathrm{Solve}\mathrm{the}\mathrm{equation}(p,q,r)\mathrm{if}\mathrm{the}\mathrm{solution}\mathrm{are}\mathrm{real}\mathrm{number}$$$$$$

Commented by i jagooll last updated on 09/May/20

$${(\sqrt[3]{\mathrm{p}}+\sqrt[3]{\mathrm{q}}+\sqrt[3]{\mathrm{r}})}^3=\sqrt{2}-1$$$$\mathrm{p}+\mathrm{q}+\mathrm{r}+3(\sqrt[3]{\mathrm{p}}+\sqrt[3]{\mathrm{q}})(\sqrt[3]{\mathrm{p}}+\sqrt[3]{\mathrm{r}})(\sqrt[3]{\mathrm{q}}+\sqrt[3]{\mathrm{r}})=\sqrt{2}-1$$$$\Rightarrow \mathrm{p}+\mathrm{q}+\mathrm{r}=-1$$$$\Rightarrow 3(\sqrt[3]{\mathrm{p}}+\sqrt[3]{\mathrm{q}})(\sqrt[3]{\mathrm{p}}+\sqrt[3]{\mathrm{r}})(\sqrt[3]{\mathrm{q}}+\sqrt[3]{\mathrm{r}})=\sqrt{2}$$

Commented by unknown last updated on 09/May/20

$$sothesolution(p,q,r)(?$$$$$$

Commented by prakash jain last updated on 12/May/20

$$\mathrm{Jagooll}\mathrm{from}\mathrm{step}2$$$$\mathrm{you}\mathrm{cannot}\mathrm{infer}$$$$p+q+r=-1\mathrm{when}p,q,r\in \mathbb{R}$$

Answered by prakash jain last updated on 12/May/20

$$\sqrt[3]{p}+\sqrt[3]{q}+\sqrt[3]{r}=\sqrt[3]{\sqrt{2}-1}$$$$\mathrm{Given}\mathrm{any}\mathrm{value}\mathrm{for}p\mathrm{and}q$$$$\mathrm{there}\mathrm{exists}\mathrm{a}\mathrm{solution}\mathrm{for}r$$$$\mathrm{for}\mathrm{example}$$$$p=1,q=1$$$$r={(\sqrt[3]{\sqrt{2}-1}-2)}^3$$$$\mathrm{There}\mathrm{are}\mathrm{infinte}\mathrm{number}\mathrm{of}\mathrm{solutions}.$$$$\mathrm{Please}\mathrm{recheck}\mathrm{question}$$

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