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# Algebra

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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