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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.

 May 21, 2021

Best Answer 

 #1
avatar+2207 
+1

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

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

(x-.5)^2 + (y-.5)^2 - .5 = 4

(x-.5)^2 + (y-.5)^2 = 4.5

The largest value of x is sqrt(4.5) + .5

 

=^._.^=

 May 21, 2021
 #1
avatar+2207 
+1
Best Answer

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

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

(x-.5)^2 + (y-.5)^2 - .5 = 4

(x-.5)^2 + (y-.5)^2 = 4.5

The largest value of x is sqrt(4.5) + .5

 

=^._.^=

catmg May 21, 2021

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