Let x and y be real numbers such that x^2 + y^2 = 4(x + y) + 12. Find the largest possible value of x.
+129845 x^2 + y^2 = 4(x + y) + 12
x^2 + y^2 = 4x + 4y + 12
x^2 - 4x + y^2 - 4y = 12 complete the square on x, y
(x^2 - 4x + 4) +( y^2 - 4y + 4 ) = 12 + 4 + 4
( x - 2)^2 + ( y -2)^2 = 20
This is a circle centered at (2,2) with a radius of sqrt (20)
The greatest value of x = 2 + sqrt (20)
