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What do I have to multiply both numerator and denominator with to get the representation is asked? $a, b, c, a_1, b_1, c_1$ are rational numbers.

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up vote 4 down vote accepted

I think, the easiest if you solve this: $$(a_1+b_1\cdot \sqrt[3]2 + c_1\sqrt[3]{2^2})(a+b\cdot \sqrt[3]2 + c\sqrt[3]{2^2}) =1 $$

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