## swin2013 2 years ago The sum of two nonegative numbers is 20. Find the numbers if...

1. swin2013

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?

2. jennychan12

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.

3. swin2013

I got y = 10

4. swin2013

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

5. swin2013

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.

6. jennychan12

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

7. swin2013

the S equation or the S' equation?

8. Hunus

the S equation

9. jennychan12

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

10. swin2013

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

11. jennychan12

x+sqrt(y) = M try that?

12. jennychan12

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