已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
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已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
已知实数x、y、z满足3x+2y+2z=17,则x^2+y^2+z^2的最小值是( )
设x^2+y^2+z^2=t
由3x+2y+2z=17得:y+z=(17-3x)/2
又y^2+z^2=t-x^2可变得:yz=(17-3x)^2/8+(x^2-t)/2
y,z可以看成m^2-[(17-3x)/2]+(17-3x)^2/8+(x^2-t)/2=0的两根
于是由判别式>=0列式得:(17-3x)^2/4-4[(17-3x)^2/8+(x^2-t)/2]>=0
化简得:t>={17(x-3)^2+136}/8
当x=3时,t取得最小值t=136/8=17即是x^2+y^2+z^2的最小值是(17)
使用线性规划,特别简单
x=3,y=2,z=2(运算结果)
Object. min Z=x^2+y^2+z^2=17
s.t. 3x+2y+2z=17
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