Find the largest value of x for which

x^2 + y^2 = x + y + 4

has a solution, if x and y are real.

Guest Apr 26, 2022

#1**+1 **

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?

BuilderBoi Apr 26, 2022