From a book I haven't read for months.

Algebra Level 3

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

The original problem is:

Solve the following system of equations:

{ 3 ( x − y ) 2 − 4 x + 8 y + 5 − x = y + 1 x 2 y + y 2 − 3 x y − 3 x + 7 y + 8 = 2 x y + 3 \large \left\{ \begin{aligned} \sqrt{3(x - y)^2 - 4x + 8y + 5} - \sqrt x &= \sqrt{y + 1}\\ x^2y + y^2 - 3xy - 3x + 7y + 8 &= 2x\sqrt{y + 3} \end{aligned} \right.

How many solutions are there?

3 4 2 1 0

Thành Đạt Lê by Thành Đạt Lê , 17, Singapore

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