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Question Number 152772 by Rankut last updated on 01/Sep/21

$$\mathit{i}\mathit{f}\sqrt[3]{\sqrt[3]{\mathit{x}-2}+2}+\sqrt[3]{2-\sqrt[3]{\mathit{x}-2}}=2$$$$\mathbf{then}\mathbf{find}\mathbf{the}\mathbf{value}\mathbf{of}$$$$\sqrt{198{\mathbf{x}}^4-868{\mathbf{x}}^3-229{\mathbf{x}}^2+200\mathbf{x}}$$

Commented by Rankut last updated on 01/Sep/21

$$anyhelpplease$$

Commented by MJS_new last updated on 01/Sep/21

$$\mathrm{typo}?$$$${\mathrm{there}}^{\prime }\mathrm{s}\mathrm{a}\mathrm{similae}\mathrm{question}...\mathrm{just}\mathrm{scroll}\mathrm{down}$$$$\mathrm{to}\mathrm{find}\mathrm{it}$$

Answered by mr W last updated on 01/Sep/21

$$lett=\sqrt[3]{x-2}$$$$\sqrt[3]{2+t}+\sqrt[3]{2-t}=2$$$$2+t+2-t+3\times 2\sqrt[3]{4-t^2}=8$$$$3\sqrt[3]{4-t^2}=2$$$$27(4-t^2)=8$$$$t=\pm \sqrt{4-\frac{8}{27}}=\pm \frac{10\sqrt{3}}{9}$$$$x=2+t^3=2\pm \frac{1000\sqrt{3}}{243}$$$$......$$

Commented by Rankut last updated on 01/Sep/21

$$thankyousir$$

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