For the last time, again.

Algebra Level 2

I don't create this problem. All of the credits go to Nguyễn Tất Thu, Đoàn Quốc Việt and Vũ Công Minh for writing these problems, and the books in general.

This is a slightly altered version of the problem:

Solve the following system of equation:

{ 2 x 2 + y 6 + y 3 = x y − ( x y ) 2 8 x y 3 + 2 y 3 − 4 x 2 + 1 ≥ 2 ( 2 x − y ) 2 + 1 \large \left\{ \begin{aligned} 2x^2 + y^6 + y^3 &= \sqrt{xy - (xy)^2}\\ 8xy^3 + 2y^3 - 4x^2 + 1 &\ge 2\sqrt{(2x - y)^2 + 1} \end{aligned} \right.

How many real solutions are there?

2 1 0 4 3

Thành Đạt Lê by Thành Đạt Lê , 17, Singapore

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