Hệ phương trình \(\left\{ {\begin{array}{*{20}{l}}{{x^2} + \left| x \right| = 2}\\{{y^2} + {x^2} - 6y = 0}\end{array}} \right.\) có bao nhiêu nghiệm?

TH1: \(\left\{ {\begin{array}{*{20}{l}}{x \ge 0}\\{{x^2} + x - 2 = 0}\\{{x^2} + {y^2} - 6y = 0}\end{array} \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{x = 1}\\{{y^2} - 6y + 1 = 0}\end{array} \Leftrightarrow \left[ {\begin{array}{*{20}{l}}{x = 1\,,\,\,y = 3 + 2\sqrt 2 }\\{x = 1\,,\,\,y = 3 - 2\sqrt 2 }\end{array}} \right.} \right.} \right.\).

TH2: \(\left\{ {\begin{array}{*{20}{l}}{x \le 0}\\{{x^2} - x - 2 = 0}\\{{x^2} + {y^2} - 6y = 0}\end{array} \Leftrightarrow \left\{ {\begin{array}{*{20}{l}}{x = - 1}\\{{y^2} - 6y + 1 = 0}\end{array} \Leftrightarrow \left[ {\begin{array}{*{20}{l}}{x = - 1\,,\,\,y = 3 + 2\sqrt 2 }\\{x = - 1\,,\,\,y = 3 - 2\sqrt 2 }\end{array}} \right.} \right.} \right.\).

Chọn D.