#### Question

If x,y are real numbers such that x^2+y^2+2 ≤ 2x+2y , find the value of x+y

Question

If x,y are real numbers such that x^2+y^2+2 ≤ 2x+2y , find the value of x+y

x^2+y^2+2 ≤ 2x+2y

x^2-2x+1+y^2-2y+1\leq 0

(x-1)^2+(y-1)^2\leq 0

Since addition of two squares is never less than 0, we get the following equation.

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

Therefore

x=1 , y=1

Finally

x+y = 2