Question 4
Determine all $a$ such that there exists unique $(x, y) \in \mathbb{R}^2$ satisfying
$$
2^{|x|} + |x| = x^2 + y + a, \quad x^2 + y^2 = 1.
$$
$$
2^{|x|} + |x| = x^2 + y + a, \quad x^2 + y^2 = 1.
$$
MathNet 2011 Question 4
Math Olympiad Vault · MathNet 2011