Let x and y be real numbers such that x^2 + y^2 = 6(x+y). Find the largest possible value of y.
+128474 x^2 + y^2 = 6(x + y)
x^2 + y^2 = 6x + 6y
x^2 - 6x + y^2 - 6y = 0 complete the square on x,y
x^2 -6x + 9 + y^2 - 6y + 9 = 9 + (
(x -3)^2 + (y - 3)^2 = 18
This is a circle with a center of (3,3) and a radius of sqrt (18)
The max value of y is 3 + sqrt (18) = 3 + 3sqrt (2)
