+343 Let x and y be real numbers such that x^2 + y^2 = 2x + 4y. Find the largest possible value of x + y.
+130493 x^2 - 2x + y^2 - 4y = 0
x^2 - 2x + 1 + y^2 - 4y + 4 = 5
(x - 1)^2 + ( y - 2)^2 = 5
max (x + y) = 1 + r cos 45 ° + 2 + r sin 45° =
1 + sqrt (5) (1/sqrt 2) + 2 + sqrt (5) (1/sqrt 2)
3 + 2 sqrt (5) / sqrt (2) =
3 + sqrt (2) * sqrt (5) =
3 + 2 sqrt (10) /2
3 + sqrt (10)
