1962 IMO Problems/Problem 4
Solve the equation .
First, note that we can write the left hand side as a cubic function of . So there are at most distinct values of that satisfy this equation. Therefore, if we find three values of that satisfy the equation and produce three different , then we found all solutions to this cubic equation (without expanding it, which is another viable option). Indeed, we find that , , and all satisfy the equation, and produce three different values of , namely , , and . So we solve . Therefore, our solutions are:
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