Question

if x,y real and x^2+y^2+2=2(x-y) then what are the values of x and y​

Answer 1

Answer:$(x,y)=(1,-1)$

Move terms to L.H.S

⬊$x^2+y^2+2-2(x-y)=0$

⬊$x^2-2x+y^2+2y+(1+1)=0$

Complete the square

⬊$(x-1)^2+(y+1)^2=0$

x-1=(real)

y+1=(real)

*(real)²≥0*

⬊$x-1=0$ Answer ∴$x=1$

⬊$y+1=0$ Answer ∴$y=-1$