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$T h e r a n g e o f x^{2} + 4 y^{2} + 9 z^{2} - 6 y z - 3 x z - 2 x y i s$

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$R$

$[0, \infty)$

$(- \infty, 0)$

$ϕ$

answer is C.

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Detailed Solution

$\begin{array}{l} f (x) = x^{2} + {(2 y)}^{2} + {(3 z)}^{2} - (2 y) (3 z) - x (3 z) - x (2 y) \\ = \frac{1}{2} [{(x - 2 y)}^{2} + {(2 y - 3 z)}^{2} + {(3 z - x)}^{2}] \geq 0 \\ ∴ f (x) \geq 0 \\ ∴ R a n g e = [0, \infty) \end{array}$

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