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Find the largest value of x for which
x^2 + y^2 = 4x + 5y
has a solution, if x and y are real.

 Aug 19, 2024
 #1
avatar+37159 
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This is the equation of a circle ....look for the right side of the circle ....

x^2 - 4x + 4      + y^2  - 5y   + 6.25 =   10.25 

(x-2)^2   + ( y- 2.5)^2   = 10.25                This is the cirlce....with center at  2,2.5    and radius sqrt (10.25) 

                                                                      the largest 'x' value will be   2 + sqrt (10.25) = 5.2015 units 

 Aug 19, 2024

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