x+y=25, x^2 + y^2 =n , find the optimize so that the two squared when added are the greatest value?

Question

I believe the answers is 0 and 25, but I wish to know how to get to these two numbers. Heres what I've tried. 
1. Y= 25-x
2. (X)^2 + (25-x)^2
3. took derv. 2x+2(25-x)(-1)
4. 2x - 50+2x=0 
5. 4x - 50=0
6. 4x=50
x =12.5

Anonymous · Accepted Answer

This passes the "sanity check" because 12.5 is just half of 25, so it makes two squares of equal size instead of a big square and a little square.  You can visualize this by drawing a graph.

x+y=25, x^2 + y^2 =n , find the optimize so that the two squared when added are the greatest value?

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