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Solve[{a*Sqrt[Pi]/2 + c*Sqrt[Pi] = 0, b*Sqrt[Pi]/2 = 0, 
  a^2*Sqrt[Pi]*3/4 + a*c*Sqrt[Pi]/2 + b^2*Sqrt[Pi]/2 + 
    a*c*Sqrt[Pi]/2 + c^2*Sqrt[Pi] = 1}, {a, b, c}]

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Set::write: Tag Plus in (a Sqrt[\[Pi]])/2+c Sqrt[\[Pi]] is Protected. >>

Set::write: Tag Times in (b Sqrt[\[Pi]])/2 is Protected. >>

Set::write: Tag Plus in (3 a^2 Sqrt[\[Pi]])/4+(b^2 Sqrt[\[Pi]])/2+1/2 a c Sqrt[\[Pi]]+1/2 a c Sqrt[\[Pi]]+c^2 Sqrt[\[Pi]] is Protected. >>