2x²+2xy+y²-6x-4y+5=o求实数x,y
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2x²+2xy+y²-6x-4y+5=o求实数x,y
2x²+2xy+y²-6x-4y+5=o
求实数x,y
2x²+2xy+y²-6x-4y+5=o求实数x,y
写成(x+y-2)^2+(x-1)^2=0
所以x=1,y=1
把5可以分成1和4
根据题计算得知X=1,Y=1
设f(x,y)=2x²+2xy+y²-6x-4y+5
x的偏导为 4x+2y-6=0
y的偏导为 2x+2y-4=0
联立解得x=1,y=1
f(x,y)最小=f(1,1)=2+2+1-6-4+5=0
所以x=1,y=1 (唯一解)
原式=(x+y-2)^2+(x-1)^2=0
x=y=1