x = ³√2+√3 , then x³+1/x³
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Step-by-step explanation:
Rationalize the denominator:
[tex]\frac{\sqrt[3]{2}+\sqrt{3}+1}{\sqrt[3]{2}+\sqrt{3}} \cdot \frac{\sqrt[3]{2}-\sqrt{3}}{\sqrt[3]{2}-\sqrt{3}}=\frac{{2}^{\frac{2}{3}}-\sqrt[3]{2}\sqrt{3}+\sqrt[3]{2}\sqrt{3}-3+\sqrt[3]{2}-\sqrt{3}}{{(\sqrt[3]{2})}^{2}-{\sqrt{3}}^{2}}
[/tex]
[tex]\frac{{2}^{\frac{2}{3}}-\sqrt[3]{2}\sqrt{3}+\sqrt[3]{2}\sqrt{3}-3+\sqrt[3]{2}-\sqrt{3}}{{(\sqrt[3]{2})}^{2}-{\sqrt{3}}^{2}}
[/tex]
[tex]
\frac{{2}^{\frac{2}{3}}-3+\sqrt[3]{2}-\sqrt{3}}{{(\sqrt[3]{2})}^{2}-{\sqrt{3}}^{2}}[/tex]