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Find the largest real number x for which there exists a real number y such that x^2 + y^2 = 2x + 2y.

michaelcai  Nov 6, 2017
 #1
avatar+537 
0

Hello michaelcai

 

This should be the answer


 

Tell me if I am wrong..

ProMagma  Nov 6, 2017
 #2
avatar+92943 
+2

x^2 + y^2  =  2x + 2y

 

x^2  - 2x  + y^2 - 2y  = 0

 

Complete the square on x and y  and we have that

 

x^2 - 2x + 1   +  y^2 -2y + 1  =  2

 

( x - 1)^2  +  (y - 1)^2  =  2

 

x will be maximized when  y = 1...so....

 

(x - 1)^2  =  2       take the positive square root

 

x - 1  =  √2

 

x =  √2 + 1

 

 

cool cool cool

CPhill  Nov 6, 2017
 #3
avatar
0

OK. I see now.

Guest Nov 6, 2017
edited by Guest  Nov 6, 2017

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