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?](/uploads/image/z/1739610-18-0.jpg?t=%E8%8B%A5%E5%AE%9E%E6%95%B0x%2Cy%2Cz%E6%BB%A1%E8%B6%B3x%EF%BC%8B2y%EF%BC%8B3z%EF%BC%9Da%EF%BC%88a%E4%B8%BA%E5%B8%B8%E6%95%B0%EF%BC%89%2C%E5%88%99x%EF%BC%BE2%EF%BC%8By%EF%BC%BE2%EF%BC%8Bz%EF%BC%BE2%E7%9A%84%E6%9C%80%E5%B0%8F%E5%80%BC%E4%B8%BA%3F)
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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