find two number so that the sum of their square is a minimum
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F.4 Math求解
2008-06-20 2:55 am
given that two positive numbers is 10
find two number so that the sum of their square is a minimum
find two number so that the sum of their square is a minimum
回答 (2)
2008-06-20 3:15 am
✔ 最佳答案
let this two number are a and b Then a+b=10
Want the min of a^2+b^2
Since b=10-a
We have
a^2+b^2
=a^2+(10-a)^2
=2a^2-20a+100
=2(a^2-10a+50)
=2[(a-5)^2+25]
So when a=b=5, the sum of their square is a minimum
a^2+b^2=5^2+5^2=50
2008-06-20 3:39 am
let x +y =10
y = 10-x
s = x^2 +y^2
s = x^2 + (10-x)^2
s = x^2 + 100 - 20x +x^2
ds/dx = 4x -20 = 0
x=5
d^2s/dx^2 = 4 > 0 so will know this is the minimum
x=5
y=5
x^2 + y^2 = 50
y = 10-x
s = x^2 +y^2
s = x^2 + (10-x)^2
s = x^2 + 100 - 20x +x^2
ds/dx = 4x -20 = 0
x=5
d^2s/dx^2 = 4 > 0 so will know this is the minimum
x=5
y=5
x^2 + y^2 = 50
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