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Rationalize the denominator of \(\displaystyle \frac{1}{\sqrt[3]{3} - \sqrt[3]{2}}\). With your answer in the form \(\displaystyle \frac{\sqrt[3]{A} + \sqrt[3]{B} + \sqrt[3]{C}}{D}\) , and the fraction in lowest terms, what is \(A + B + C + D\)?

 

Please help and thank you so much! Also, could you write the steps that you did to get your answer because I want to learn how to do it myself~

 Dec 5, 2020
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(a^3 + b^3) = (a + b)(a^2 - ab + b^2)

==> 1/(cbrt(3) - cbrt(2)) = (4^(1/3) + 12^(1/3) + 36^(1/3))/3, so A + B + C + D = 55.

 Dec 5, 2020

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