Find two numbers adding to 20 such that the sum of their squares is as small as possible.

Question

Find two numbers adding to 20 such that the sum of their squares  is as small as possible.

google · Answer

x+y = 20
minimize x^2+y^2

google · Answer

y = 20-x
f(x) = x^2 + (20-x)^2 = x^2 + 400 - 40x + x^2

google · Answer

differentiate:
f'(x) = 2x -40 + 2x = 0,
solve for x. x = 10

google · Answer

test if it's a min: f''(x) = 4 > 0, so x=10 is a min.

google · Answer

y = 20-x=20-10=10

anonymous · Answer

Thanks a ton I can see where I mess up

google · Answer

np, i thought i was messing up too somewhere.. i kept getting 0 for y' for some reason

anonymous · Answer

me too

anonymous · Answer

bet anything you make them equal right?

anonymous · Answer

yes

anonymous · Answer

calc will work but you can argue by symmetry, since  you cannot tell the difference between x and y

anonymous · Answer

$$x^2+y^2$$
$$x+y=20$$ switch x and y and get 
$$y^2+x^2$$
$$y+x=20$$ meaning you cannot tell the difference between x and y

anonymous · Answer

just thought i would mention it