Question

Układ równań:
(x-1)potęga2 - (y+2)potęga2 =(x-y)(x+y)
2x+y=0

Answer 1

(x-1)2-(y+2)2=(x-y)(x+y)
2x+y=0
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x2-2x+1-y2-4y-4=x2-y2 /-x2+y2
2x+y=0
______________________________________________
-2x-3-4y=0 /+3
2x+y=0
______________________________
-2x-4y=3
2x+y=0
_________________________
dodajemy stronami
-3y=3 /:(-3)
y=-1
2x-1=0
___________________________
y=-1
2x=1 /:2
_____________________________--
y=-1
x=1/2

Answer 2

{ (x - 1)² - (y + 2)² = (x - y)(x + y)
{ 2x + y = 0

{ x² - 2x + 1 - (y² + 4y + 4) = x² - y²
{ 2x + y = 0

{ x² - 2x + 1 - y² - 4y - 4 - x² + y² = 0
{ 2x + y = 0

{ - 2x - 4y - 3 = 0
{ 2x + y = 0

{ - 2x - 4y = 3
{ 2x + y = 0
_____________
- 3y = 3 /:(- 3)
y = - 1

2x + y = 0
2x - 1 = 0
2x = 1 /:2
x = ½

{ x = ½
{ y = - 1