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MathNet 2017-part-03 — 176 problems (EN–VI) Question 148

Math Olympiad Vault · MathNet 2017-part-03 — 176 problems (EN–VI)

Question 148

How many pairs of real numbers $(x, y)$ satisfy both equations $x + y^{2} = y^{3}$ and $y + x^{2} = x^{3}$?

(A) 1
(B) 3
(C) 5
(D) 9
(E) Infinitely many