1977 AHSME Problems/Problem 23
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If the solutions of the equation are the cubes of the solutions of the equation , then
Solution
Let and be the roots of the equation . Then, and are the roots of . Applying Vieta's Formulas to the first equation, we have and . Similarly, from the second equation, we have and . Cubing , we get . Plugging in from the other equations gives . Rearranging we have