5x+6y+7z=1,则x^2+y^2+z^2+(x+y+z)^2的最小值为

w=x^2+y^2+z^2+(x+y+z)^2+t(5x+6y+7z-1)
&w/&x=2x+2(x+y+z)+5t=0 (1)
&w/&y=2y+2(x+y+z)+6t=0 (2)
&w/&z=2z+2(x+y+z)+7t=0 (3)
5x+6y+7z=1 (4)
联立(1)(2)(3)(4) 解得 x=1/58 y=3/58 z=5/58 t=-2/29
得到唯一的可能极值点
最小值wmin=(1/58)^2+(3/58)^2+(5/58)^2+(1/58+3/58+5/58)^2=1/29

^2是不是√2