Find the largest real number x for which there exists a real number y such that x^2 + y^2 = 2x + y.
+128460 x^2 + y^2 = 2x + y
x^2 - 2x + y^2 - y = 0 complete the square on x and y
x^2 - 2x + 1 + y^2 - y + 1/4 = 1 + 1/4 factor
(x - 1)^2 + ( y - 1/2)^2 = 5/4
This is a circle with a center of (1, 1/2) and a radius of sqrt (5/4) = sqrt (5) / 2
So.....the largest x that will provide a real numer for y is when x = (1 + sqrt (5)/2)
