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Problem 8 of Second round

Source: XI International Festival of Young Mathematicians Sozopol 2022, Theme for 11-12 grade

September 9, 2022
algebra

Problem Statement

Let xx be a real number. Find the greatest possible value of the following expression:
47x43+43x47−2021x\frac{47^x}{\sqrt{43}}+\frac{43^x}{\sqrt{47}}-2021^x.
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