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et x and y be real numbers such that x^2 + y^2 = 4(x + y) + 16. Find the largest possible value of x.

 Jun 29, 2022
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Rearrange as

 

x^2 - 4x + y^2 - 4y =  16          complete the square on x.y

 

x^2 - 4x + 4  + y^2 - 4y + 4 =  16 + 4 + 4

 

(x - 2)^2  + ( y - 2)^2 =   24

 

This is a circle centered at   (2, 2)  with a radius of sqrt (24)  =  2sqrt (6)

 

The greatest value for  x =   

 

2  + 2sqrt (6)  = 

 

 2 ( 1 + sqrt (6) )

 

 

 

cool cool cool

 Jun 29, 2022

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