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MathNet 2006 — Part 02 Question 77

Math Olympiad Vault · MathNet 2006 — Part 02

Question 77

Solve the equation
$$
\log_{a}\left(a^{2\left(x^{2}+x\right)}+a^{2}\right)=x^{2}+x+\log_{a}\left(a^{2}+1\right)
$$
where $a$ is a real number.