The sum of two positives is 10,find the two numbers so that the sum of their squares is a minimum.
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我想係用列式方法去計
Maths
2008-10-23 1:27 am
這一條數唔知點樣做
The sum of two positives is 10,find the two numbers so that the sum of their squares is a minimum.
The sum of two positives is 10,find the two numbers so that the sum of their squares is a minimum.
回答 (2)
2008-10-27 1:47 am
✔ 最佳答案
Let two number are x,10-x.x2+(10-x)^2
=x2+(100-20x+x2)
=2x2-20x+100
=2(x2-10x)+100
=2(x2-10x+25)+100-50
=2(x-5)2+50
∴ the sum of their squares is a minimum=50
2008-10-23 1:40 am
The sum of two positives that is 10:
1, 9
2 , 8
3 , 7
4 , 6
5 , 5
the sum of their squares:
82
68
58
52
50<
since 50 is the minimum;
therefore the two positives are 5 & 5.
1, 9
2 , 8
3 , 7
4 , 6
5 , 5
the sum of their squares:
82
68
58
52
50<
since 50 is the minimum;
therefore the two positives are 5 & 5.
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