Question

x = ³√2+√3 , then x³+1/x³​

Answer 1

Step-by-step explanation:

Rationalize the denominator:

$\frac{\sqrt[3]{2}+\sqrt{3}+1}{\sqrt[3]{2}+\sqrt{3}} \cdot \frac{\sqrt[3]{2}-\sqrt{3}}{\sqrt[3]{2}-\sqrt{3}}=\frac{{2}^{\frac{2}{3}}-\sqrt[3]{2}\sqrt{3}+\sqrt[3]{2}\sqrt{3}-3+\sqrt[3]{2}-\sqrt{3}}{{(\sqrt[3]{2})}^{2}-{\sqrt{3}}^{2}} </p><p>$

$\frac{{2}^{\frac{2}{3}}-\sqrt[3]{2}\sqrt{3}+\sqrt[3]{2}\sqrt{3}-3+\sqrt[3]{2}-\sqrt{3}}{{(\sqrt[3]{2})}^{2}-{\sqrt{3}}^{2}}</p><p>$

$</p><p>\frac{{2}^{\frac{2}{3}}-3+\sqrt[3]{2}-\sqrt{3}}{{(\sqrt[3]{2})}^{2}-{\sqrt{3}}^{2}}$