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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.

 Jun 12, 2024

Best Answer 

 #1
avatar+1946 
+1

Notice that x2+y2=4x+5y is very similar to the equation of a circle. 

We have x24x+y25y=0

 

Now, completing the square for both x and y, we get

(x2)2+(y5/2)2=25/4+16

 

This is the official equation of a circle. 

It has the center at (2,5/2) and a radius of 89/4

 

The largest value of x is basically the x value of the center added to the radius. 

 

Thus, we have 2+892=4+892

 

So our final answer is 4+892

 

Thanks! :)

 Jun 12, 2024
 #1
avatar+1946 
+1
Best Answer

Notice that x2+y2=4x+5y is very similar to the equation of a circle. 

We have x24x+y25y=0

 

Now, completing the square for both x and y, we get

(x2)2+(y5/2)2=25/4+16

 

This is the official equation of a circle. 

It has the center at (2,5/2) and a radius of 89/4

 

The largest value of x is basically the x value of the center added to the radius. 

 

Thus, we have 2+892=4+892

 

So our final answer is 4+892

 

Thanks! :)

NotThatSmart Jun 12, 2024

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