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Find the largest value of x for which

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

has a solution, if x and y are real.

 Apr 26, 2022
 #1
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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?

 Apr 26, 2022

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