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As x,y,zx, y, zx,y,z ranges over all possible real numbers, what is the minimum value of
3x2+12y2+27z2−4xy−12yz−6xz−8y−24z+100? 3x^2+12y^2+27z^2-4xy-12yz-6xz-8y-24z+100 ? 3x2+12y2+27z2−4xy−12yz−6xz−8y−24z+100?
This problem has been proposed by Hui.
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