SOLUTION: Two numbers have a sum of 20. If the sum of their squares is a minimum, find the numbers. Please & Thank you so much.

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Two numbers have a sum of 20. If the sum of their squares is a minimum, find the numbers. Please & Thank you so much.      Log On


   

Question 274640: Two numbers have a sum of 20. If the sum of their squares is a minimum, find the numbers.
Please & Thank you so much.
Answer by JBarnum(2146) About Me  (Show Source):
You can put this solution on YOUR website!
m=minimum
i get
a%2Bb=20
a%5E2%2Bb%5E2=m m has to equal 20%5E2 for the 2 equations to be accurate
%2820-b%29%5E2%2Bb%5E2=400
%28400-2b%2Bb%5E2%29%2Bb%5E2=400
2b%5E2-2b=0
2%28b-1%29%28b-0%29=0
b=1,0; b has to =0 in order for a%2Bb=20 anda%5E2%2Bb%5E2=400 to coexist because if a=19 and b=1 then the second eqation doesnt work so if a=20 and b=0 then everything will work.
my answers are
highlight%28a=20%29
highlight%28b=0%29