Find the largest value of x for which
x^2 + y^2 = x + y + 4
has a solution, if x and y are real.
+2668 Rearrange as: \(x^2-x+y^2-y=4\)
Completing the square, we have: \((x-0.5)^2+(y-0.5)^2=4.5\)
The largest value of x is the center x co-ordinate + the radius
The center of the circle is 0.5 and the radius is \(\sqrt{4.5}\)
Can you take it from here?
