设实数x,y,z满足x+y+2z=6,求的x*x+y*y+z*z最小值,并求此时x,y,z的值.

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设实数x,y,z满足x+y+2z=6,求的x*x+y*y+z*z最小值,并求此时x,y,z的值.
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设实数x,y,z满足x+y+2z=6,求的x*x+y*y+z*z最小值,并求此时x,y,z的值.
设实数x,y,z满足x+y+2z=6,求的x*x+y*y+z*z最小值,并求此时x,y,z的值.

设实数x,y,z满足x+y+2z=6,求的x*x+y*y+z*z最小值,并求此时x,y,z的值.
由柯西不等式
(x²+ y² +z²)*(1+ 1+ 4)=6(x²+ y²+z²)≥(x+ y+ 2z)²=36即x²+y²+z²≥1/6等号在x:y:z=1:1:4取得成立 x=y=z/4即z=12/5 ,x=y=3/5