Question

Решите систему уравнений, ! желательно с объяснениями заранее !
х2+у2=5,
х+у=3

Answer 1

$\left \{ {{x^{2}+y^{2}=5} \atop {x+y=3}} \right. \\\\\left \{ {{y=3-x} \atop {x^{2}+(3-x)^{2}=5}} \right.\\\\\left \{ {{y=3-x} \atop {x^{2}+9-6x+x^{2}=5}} \right.\\\\\left \{ {{y=3-x} \atop {2x^{2}-6x+4=0 }} \right.\\\\\left \{ {{y=3-x} \atop {x^{2}-3x+2=0 }} \right.\\\\x^{2}-3x+2=0\\\\x_{1}=1\\\\x_{2}=2-teorema.Vieta\\\\y_{1}=3-1=2\\\\y_{2}=3-2=1\\\\Otvet:\boxed{(1;2),(2;1)}$