What is the least value of the expression ? #x^2 + 4y^2 + 3z^2 - 2x - 12y - 6z + 14#

1 Answer
Ananda Dasgupta
Feb 18, 2018

1

Explanation:

The given expression can be written in the form

#(x^2-2x+1)+4(y^2-2times 3/2 times y+9/4)+3(z^2-2z+1)+14-1-9-3#
#=(x-1)^2+4(y-3/2)^2+3(z-1)^2+1#

Since the first three terms of this expression can not be negative, the smallest value that the expression can attain is 1.

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