Round about

Algebra Level 5

A set of four distinct real numbers is called round if it satisfies {x12+x2=2,x22+x3=2,x32+x4=2,x42+x1=2, \begin{cases} x_1^2+x_2=2,\\ x_2^2+x_3=2,\\ x_3^2+x_4=2,\\ x_4^2+x_1=2,\\ \end{cases} and x1=min(x1,x2,x3,x4) x_1 = \min (x_1, x_2, x_3, x_4 ) .

How many round sets are there?

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