x、y为实数,求5x²+2y²-2xy-4x-4y+9的最小值
人气:273 ℃ 时间:2019-12-09 10:12:07
解答
5x²+2y²-2xy-4x-4y+9=
4(x²-x)+(y²-4y+4)+(x²-2xy+y²)+5=
4(x²-x+1/4)+(y²-4y+4)+(x²-2xy+y²)+4=
4(x - 1/2)² + (y - 2)² + (x - y)² + 4
x=y=1
最小值:4+2=6当x=0.5,y=1.25时,原式=5.125!原来如此,我想错了。x=1/2y-2 = x - y2y=2.5y=1.25才对的。不好意思了。。那为什么这样最小我也不知道,不好意思。看你精神可嘉,给你吧我现在知道了
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