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MathNet 2004 — Part 01 Question 48

Math Olympiad Vault · MathNet 2004 — Part 01

Question 48

Find all values of $a$ such that the equation
$$
4^{x} - (a^{2} + 3a - 2) 2^{x} + 3a^{3} - 2a^{2} = 0
$$
has a unique solution.