et x and y be real numbers such that x^2 + y^2 = 4(x + y) + 16. Find the largest possible value of x.
+128474 Rearrange as
x^2 - 4x + y^2 - 4y = 16 complete the square on x.y
x^2 - 4x + 4 + y^2 - 4y + 4 = 16 + 4 + 4
(x - 2)^2 + ( y - 2)^2 = 24
This is a circle centered at (2, 2) with a radius of sqrt (24) = 2sqrt (6)
The greatest value for x =
2 + 2sqrt (6) =
2 ( 1 + sqrt (6) )
