Решить систему уравнений (x+y=6)(xy=-7)

[latex] \left \{ {{x+y=6} \atop {xy=-7}} \right. \Longleftrightarrow \left \{ {{x=6-y} \atop {(6-y)y=-7}} \right. \Longleftrightarrow \left \{ {{x=6-y} \atop {6y-y^2=-7}} \right. \Longleftrightarrow \left \{ {{x=6-y} \atop {6y-y^2+7=0}} \right. \Longleftrightarrow \\ \Longleftrightarrow \left \{ {{x=6-y} \atop {-y^2+6y+7=0}} \right. \Longleftrightarrow \left \{ {{x=6-y} \atop {y=-1}} \right. \Longleftrightarrow \left \{ {{x=6-(-1)} \atop {y=-1}} \right. \Longleftrightarrow [/latex] [latex]\Longleftrightarrow \boxed{ \left \{ {{x=7} \atop {y=-1}} \right.} [/latex]

х+у=6. у=6-х. у=6-х. у=6-х ху=-7. ху=-7 х(6-х)=-7 6х-х²=-7 6х-х²=-7 6х-х²+7=0 -х²+6х+7=0 х²-6х-7=0 D=(-6)²-4*1*(-7)=36+28=√64=8>0 х1=6+8/2=7 х2=6-8/2=-1 х=7 у=6-7=-1