Question

Rezolvati in R ecuatia: x la 2+ y la 2+ 8x+4y= -20

Answer 1

x²+y²+8x+4y+20=0
x²+8x+16+  y²+4y+4= 0
(x+4)²+(y+2)²= 0
ecuatie adevarata doar cand ambii termeni sunt zero
deci x=-4 si y=-2

O zi buna!

Answer 2

x^2+y^2+8x+4y=-20(+20)
x^2+y^2+8x+4y=0
20=16+4
Grupam convenabili termenii
(x^2+8x+16)+(y^2+4y+4)=0
(a+b)^2=a^2+2ab+b^2
x^2+8x+16=x^2+4x+4x+4^2=(x+4)^2
y^2+4y+4=y^2+2y+2y+2^2=(y+2)^2
(x+4)^2+(y+2)^2=0
Deoarece orice x^2>=0
0+0=0
(x+4)^2=0
x+4=0
x=0-4
x=-4
(y+2)^2=0
y+2=0
y=0-2
y=-2
{x,y}={-4,-2}