若实数x,y,z满足x+2y+3z=a(a为常数),则x^2+y^2+z^2的最小值为?

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若实数x,y,z满足x+2y+3z=a(a为常数),则x^2+y^2+z^2的最小值为?

若实数x,y,z满足x+2y+3z=a(a为常数),则x^2+y^2+z^2的最小值为?
若实数x,y,z满足x+2y+3z=a(a为常数),则x^2+y^2+z^2的最小值为?

若实数x,y,z满足x+2y+3z=a(a为常数),则x^2+y^2+z^2的最小值为?
a^2/14
用柯西不等式
(x^2+y^2+z^2)*(1+4+9)>=(x+2y+3z)^2=a^2
所以x^2+y^2+z^2>=a^2/14 (当且仅当x=y/2=z/3 即x=a/14 y=a/7 z=3a/14时取等)

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