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Question: Solve system in real domain with Maple

My attempt:

RealDomain[solve]({x^2+y^2+z^2 = 3, x+y+z = 3}, {x,y,z});

             {x = -RootOf(_Z^2+(z-3)*_Z+z^2-3*z+3)-z+3, y = RootOf(_Z^2+(z-3)*_Z+z^2-3*z+3), z = z}

 

In fact, the system in the real domain has a unique solution x = 1, y = 1, z = 1. It is easy to find by hand, noting that the plane  x + y + z = 3  is tangent to the sphere  x^2 + y^2 + z^2 = 3 .

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