Find two numbers such that their sum is 20 and the sum of their squares is a minimum.
2006-11-27 14:36:07 · 3 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
You're right that this is a parabola problem. The specific parabola is:
f(x) = x^2 + (20 - x)^2 = 2x^2 - 40x + 400
Now, if you are taking calculus, just find the value where the first derivative is zero. If you aren't in calculus yet, the minimum value is the bottom of the parabola.
2006-11-27 14:43:12 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Looks like 10 and 10 (200), or 9 and 11 (202) if they have to be two different numbers.
2006-11-27 22:40:02 · answer #2 · answered by Amy F 5 · 0⤊ 0⤋
the nos are x and 20-x
sum of the squaresS=x^2+(20-x)^2
dS/dx=2x-2(20-x)
setting this to zero for min
2x-40+2x=0
4x=20
x=5
the nos are 5 and 15
2006-11-27 22:40:07 · answer #3 · answered by raj 7 · 0⤊ 0⤋