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Question Number 156966 by Armindo last updated on 17/Oct/21

Commented by Armindo last updated on 17/Oct/21

Helô, I need help...

Answered by Rasheed.Sindhi last updated on 18/Oct/21

$$\frac{\sqrt[3]{9}-1}{\sqrt[3]{3}-1}=\frac{{\left(\sqrt[3]{3}\right)}^2-1}{\sqrt[3]{3}-1}=\frac{\cancel{(\sqrt[3]{3}-1)}(\sqrt[3]{3}+1)}{\cancel{\sqrt[3]{3}-1}}$$$$=\sqrt[3]{3}+1$$

Answered by depressiveshrek last updated on 18/Oct/21

$$\frac{\sqrt[3]{9}-1}{\sqrt[3]{3}-1}$$$$$$$$\frac{\sqrt[3]{9}-1}{\sqrt[3]{3}-1}\times \frac{\sqrt[3]{9}+\sqrt[3]{3}+1}{\sqrt[3]{9}+\sqrt[3]{3}+1}$$$$$$$$\frac{(\sqrt[3]{9}-1)(\sqrt[3]{9}+\sqrt[3]{3}+1)}{(\sqrt[3]{3}-1)(\sqrt[3]{9}+\sqrt[3]{3}+1)}$$$$$$$$\frac{\sqrt[3]{9}(\sqrt[3]{9}+\sqrt[3]{3}+1)-(\sqrt[3]{9}+\sqrt[3]{3}+1)}{\sqrt[3]{3^3}-1^3}$$$$$$$$\frac{\sqrt[3]{9\ast 9}+\sqrt[3]{9\ast 3}+\sqrt[3]{9}-\sqrt[3]{9}-\sqrt[3]{3}-1}{3-1}$$$$$$$$\frac{\sqrt[3]{81}+\sqrt[3]{27}-\sqrt[3]{3}-1}{2}$$$$$$$$\frac{\sqrt[3]{3^3\ast 3}+3-\sqrt[3]{3}-1}{2}$$$$$$$$\frac{\sqrt[3]{3^3}\ast \sqrt[3]{3}-\sqrt[3]{3}+2}{2}$$$$$$$$\frac{3\sqrt[3]{3}-\sqrt[3]{3}+2}{2}$$$$$$$$\frac{2\sqrt[3]{3}+2}{2}$$$$$$$$\frac{2(\sqrt[3]{3}+1)}{2}$$$$$$$$\sqrt[3]{3}+1$$$$$$$$$$$$$$$$$$$$$$$$\frac{1}{\sqrt[4]{5}-\sqrt[4]{2}}$$$$$$$$\frac{1}{\sqrt[4]{5}-\sqrt[4]{2}}\times \frac{\sqrt[4]{5}+\sqrt[4]{2}}{\sqrt[4]{5}+\sqrt{2}}$$$$$$$$\frac{\sqrt[4]{5}+\sqrt[4]{2}}{(\sqrt[4]{5}-\sqrt[4]{2})(\sqrt[4]{5}+\sqrt[4]{2})}$$$$$$$$\frac{\sqrt[4]{5}+\sqrt[4]{2}}{\sqrt[4]{5^2}-\sqrt[4]{2^2}}$$$$$$$$\frac{\sqrt[4]{5}+\sqrt[4]{2}}{\sqrt{5}-\sqrt{2}}$$$$$$$$\frac{\sqrt[4]{5}+\sqrt[4]{2}}{\sqrt{5}-\sqrt{2}}\times \frac{\sqrt{5}+\sqrt{2}}{\sqrt{5}+\sqrt{2}}$$$$$$$$\frac{(\sqrt[4]{5}+\sqrt[4]{2})(\sqrt{5}+\sqrt{2})}{(\sqrt{5}-\sqrt{2})(\sqrt{5}+\sqrt{2})}$$$$$$$$\frac{\sqrt[4]{5}\sqrt{5}+\sqrt[4]{5}\sqrt{2}+\sqrt[4]{2}\sqrt{5}+\sqrt[4]{2}\sqrt{2}}{\sqrt{5^2}-\sqrt{2^2}}$$$$$$$$\frac{\sqrt[4]{5}\sqrt[4]{5^2}+\sqrt[4]{5}\sqrt[4]{2^2}+\sqrt[4]{2}\sqrt[4]{5^2}+\sqrt[4]{2}\sqrt[4]{2^2}}{5-2}$$$$$$$$\frac{\sqrt[4]{5\ast 5^2}+\sqrt[4]{5\ast 2^2}+\sqrt[4]{2\ast 5^2}+\sqrt[4]{2\ast 2^2}}{3}$$$$$$$$\frac{\sqrt[4]{5^3}+\sqrt[4]{5\ast 4}+\sqrt[4]{2\ast 25}+\sqrt[4]{2\ast 4}}{3}$$$$$$$$\frac{\sqrt[4]{125}+\sqrt[4]{20}+\sqrt[4]{50}+\sqrt[4]{8}}{3}$$$$$$$$\frac{\sqrt[4]{5^2\ast 5}+\sqrt[4]{2^2\ast 5}+\sqrt[4]{5^2\ast 2}+\sqrt[4]{2^2\ast 2}}{3}$$$$$$$$\frac{\sqrt[4]{5^2}\sqrt[4]{5}+\sqrt[4]{2^2}\sqrt[4]{5}+\sqrt[4]{5^2}\sqrt[4]{2}+\sqrt[4]{2^2}\sqrt[4]{2}}{3}$$$$$$$$\frac{\sqrt{5}\sqrt[4]{5}+\sqrt{2}\sqrt[4]{5}+\sqrt{5}\sqrt[4]{2}+\sqrt{2}\sqrt[4]{2}}{3}$$$$$$

Commented by Armindo last updated on 18/Oct/21

thanks...I will check the procedure! do you have a book, when I find that solve or This procedure?

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