有人識計嗎=.=??
更新1:
計到了=.= 搵個人來打D字- . - 我給個最佳回答你@@
中四MATHS題=0=
2008-10-16 3:44 am
Given that the sum of two numbers is 20 , find the minimum value of the sum of the squares of these two numbers.
有人識計嗎=.=??
有人識計嗎=.=??
回答 (2)
2008-10-16 7:35 am
✔ 最佳答案
Let x be a smaller number, then the bigger one = 20 - xthe sum of the squares
= x^2 + (20 - x)^2
=x^2 + 400 - 40x + x^2
=2x^2 - 40x + 400
=2(x^2 - 20x) + 400
=2(x^2 - 20x + 100 - 100) + 400
=2[(x - 10)^2 - 100] + 400
=2(x - 10)^2 - 200 + 400
=2(x - 10)^2 + 200
Therefore, the minimum value of the sum of the squares = 200
參考: Myself
2008-10-16 5:59 pm
Let x be a smaller number, then the bigger one = 20 - x
the sum of the squares
= x^2 + (20 - x)^2
=x^2 + 400 - 40x + x^2
=2x^2 - 40x + 400
=2(x^2 - 20x) + 400
=2(x^2 - 20x + 100 - 100) + 400
=2[(x - 10)^2 - 100] + 400
=2(x - 10)^2 - 200 + 400
=2(x - 10)^2 + 200
Therefore, the minimum value of the sum of the squares = 200
Hope I can help you.
the sum of the squares
= x^2 + (20 - x)^2
=x^2 + 400 - 40x + x^2
=2x^2 - 40x + 400
=2(x^2 - 20x) + 400
=2(x^2 - 20x + 100 - 100) + 400
=2[(x - 10)^2 - 100] + 400
=2(x - 10)^2 - 200 + 400
=2(x - 10)^2 + 200
Therefore, the minimum value of the sum of the squares = 200
Hope I can help you.
參考: my maths knowledge
收錄日期: 2021-04-19 20:39:33
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20081015000051KK01627