若2x-3y+z=3,求x^2+(y-1)^2+z^2的最小值
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若2x-3y+z=3,求x^2+(y-1)^2+z^2的最小值
若2x-3y+z=3,求x^2+(y-1)^2+z^2的最小值
若2x-3y+z=3,求x^2+(y-1)^2+z^2的最小值
2x-3y+z=3
f(x,y,z) = x^2+(y-1)^2+z^2 - t (2x-3y+z-3)
f'(x) = 2x-2t = 0
f'(y) = 2(y-1) + 3t = 0
f'(z) = 2z - t=0
求解得t=6/7
此时最小值为46/49
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