Solution
= Solution
This can be false. For any nonzero <transcendental number> $\beta$, the number $\gamma=1/\beta$ is also transcendental, since otherwise its reciprocal would be <algebraic number>[algebraic]. Yet $\beta\gamma=1$ is algebraic.
= Solution
This can be false. For any nonzero <transcendental number> $\beta$, the number $\gamma=1/\beta$ is also transcendental, since otherwise its reciprocal would be <algebraic number>[algebraic]. Yet $\beta\gamma=1$ is algebraic.