Question

mam klopoty z matma moze mogl mi ktos pomuc rozwiazac te zadanie
(x-1)(x-1)-(y-2)(y-2)=(x-y)(x+y)

2x+y=0

Answer 1

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

2x+y=0

 

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

y=-2x

 

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

y=-2x

 

x2-x2-y2+y2-2x+4y=3

y=-2x

 

-2x+4y=3

y=-2x

 

-2x+4*(-2x)=3

y=-2x

 

-2x-8x=3

y=-2x

 

-10x=3

y=-2x

 

x=- 3/10

y=-2*(-3/10)=6/10

 

x=-3/10

y=6/10= 3/5

metoda przeciwnych współczynników

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

2x+y=0

 

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

2x+y=0

 

-2x+4y=3

2x+y=0

..................

5y=3

y=3/5

 

2x+y=0

2x+3/5=0

2x=-3/5

x=-3/10

 

x=-3/10

y=3/5