+0  
 
0
80
1
avatar

Let x and y be real numbers such that x^2 + y^2 = 4(x + y) + 12. Find the largest possible value of x.

 Jul 28, 2022
 #1
avatar+124676 
+1

x^2 + y^2  = 4(x + y)  + 12

 

x^2 + y^2  = 4x + 4y + 12

 

x^2 - 4x + y^2 - 4y  = 12       complete  the square on x, y

 

(x^2  - 4x  + 4)  +( y^2 - 4y + 4 )   =   12 + 4 + 4

 

( x - 2)^2  + ( y -2)^2 =   20

 

This is a circle centered at (2,2)  with a radius of sqrt (20)

 

The greatest value of  x =    2 + sqrt (20)

 

 

cool cool cool

 Jul 28, 2022

33 Online Users

avatar
avatar
avatar