Question

x+y=-1, xy=-2
va rog rezolvati sistemul de ecuatii

Answer 1

{x+y=-1
{xy=-2
Observam ca: S=x+y=-1 si P=xy=-2.
Putem forma o ecuatie de gradul doi care are drept solutii pe x si y.
t²-St+P=0
t²+t-2=0
Acum ori observam descopunerea directa:
(t+2)(t-1)=0 
t+2=0 => t=-2
t-1=0 => t=1
Sau calculam delta:
Δ=1-4*(-2)=9
t1=(-1+3)/2=2/2=1
t2=(-1-3)/2=-4/2=-2
Si concluzionam:
(x,y)∈{(1;-2);(-2;1)}.

Answer 2

x+y= -1
xy= -2 

x= -1-y 
(-1-y)*y= -2 

x= -1-y 
-y-y^2= -2 

x= -1-y
-y^2-y+2=0 (rezolvam cu delta) 

delta=b^2-4ac= 1+8=9
y1=(-b+Vdelta)/2a=(1+3)/-2= -4/2= -2 
y2= (-b-Vdelta)/2a=(1-3)/-2= -4/-2=2

x= -1-y
y= -2 sau 2 

x= -1+2 sau x= -1-2
y= -2 sau 2 

x= 1 sau -3 
y= -2 sau 2