Question

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

Answer 1

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

Answer 2

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