數學問題 幫忙謝謝?
回答 (4)
2017-08-03 10:50 pm
✔ 最佳答案
x+y=30y=30-x
x^2+y^2
=x^2+(30-x)^2
=2x^2-60x+900
=2(x-15)^2+450
x=y=15 時, 有極小值 450 ....Ans
2017-08-03 10:54 pm
x^2+y^2
=x^2+(30-x)^2
=x^2+900-60x+x^2
=2x^2-60x+900
=2(x^2-30x)+900
=2(x^2-30x+225-225)+900
=2(x-15)^2-450+900
=2(x-15)^2+450
x^2+y^2的極小值=2(0)+450=450
=x^2+(30-x)^2
=x^2+900-60x+x^2
=2x^2-60x+900
=2(x^2-30x)+900
=2(x^2-30x+225-225)+900
=2(x-15)^2-450+900
=2(x-15)^2+450
x^2+y^2的極小值=2(0)+450=450
2017-08-04 6:58 am
Let A = x^2 + y^2 = x^2 + (30 - x)^2 = x^2 + 900 + x^2 - 60x. That is A = 2x^2 -60x + 900 = 2(x^2 - 30x + 450) = 2[(x - 15)^2 - 225 + 450] = 2(x - 15)^2 + 450. So max. value of x^2 + y^2 = 450 when x = 15. Correction : should be min. value, not max. value.
2017-08-03 10:51 pm
用算幾不等式a+b>=2√ab
可以找到xy=225
再用(x+y)^2=900=x^2+y^2+2xy=x^2+y^2+450
所以x^2+y^2極值等於450
可以找到xy=225
再用(x+y)^2=900=x^2+y^2+2xy=x^2+y^2+450
所以x^2+y^2極值等於450
收錄日期: 2021-04-18 17:31:36
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