Minimum simplification!

Algebra Level 3

What is the minimum value of the expression below? x 2 + 4 y 2 + 3 z 2 − 2 x − 12 y − 6 z + 14 x^2 + 4y^2 + 3z^2 - 2x - 12y - 6z + 14


The answer is 1.

Skanda Prasad by Skanda Prasad , 20, India

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1 solution

Vilakshan Gupta
Aug 25, 2017

The expression can be Rewritten as ( x − 1 ) 2 + ( 2 y − 3 ) 2 + 3 ( z − 1 ) 2 + 1 (x-1)^2+(2y-3)^2+3(z-1)^2+1 Assuming x , y , z ∈ R x,y,z \in \mathbb{R} .Least value of a squared expression is 0 0 , therefore minimum value of the expression occurs when x = 1 x=1 , y = 3 2 y=\frac{3}{2} , z = 1 z=1 , which is 1 \boxed{1}

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