The sum of two nonegative numbers is 20. Find the numbers if...

Question

anonymous · Answer

a) the sum of their squares is a large as possible; as small as possible?

b) one number plus the square root of the other is a large as possible; as small as possible?

jennychan12 · Answer

i only know how to do this with optimization (calculus)
x^2+y^2 =M
x+y = 20 
Find y in terms of x and plug it in, then take the derivative.

anonymous · Answer

I got y = 10

anonymous · Answer

so that's the minimum? but i don't know how to find the largest possible answer

anonymous · Answer

no, i did it your previous way lol. I put the primary equation as x^2+y^2= S
and the secondary equation as x+y=20 but idk if that's correct.

jennychan12 · Answer

yeah, that's correct, then solve for one of the variables and plug it into the S equation

anonymous · Answer

the S equation or the S' equation?

hunus · Answer

the S equation

jennychan12 · Answer

plug it into the S equation, simplify
then take the derivative (S')

anonymous · Answer

Oh i figured it out lol!!! But i don't know how to solve for part b :(

jennychan12 · Answer

x+sqrt(y) = M try that?

jennychan12 · Answer

using x+y = 20 
plug in, same things...?
dunno if it'll work, but....