Chứng minh 4x^2+y^2 +z^2 +14 >= 12x-2y-4z

Question

Chứng minh 4x^2+y^2 +z^2 +14 >= 12x-2y-4z

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Autumn 40 phút 2021-10-04T04:59:25+00:00 2 Answers 0 views 0

Answers ( )

    0
    2021-10-04T05:00:37+00:00

    Đáp án:

    (2x−3)2+(y−1)2+(z−2)2≥0.

    0
    2021-10-04T05:00:52+00:00

    \[\begin{array}{l}
    4{x^2} + {y^2} + {z^2} + 14 \ge 12x – 2y – 4z\\
    \Leftrightarrow 4{x^2} – 12x + {y^2} – 2y + {z^2} – 4z + 14 \ge 0\\
    \Leftrightarrow 4{x^2} – 12x + 9 + {y^2} – 2y + 1 + {z^2} – 4z + 4 \ge 0\\
    \Leftrightarrow {\left( {2x – 3} \right)^2} + {\left( {y – 1} \right)^2} + {\left( {z – 2} \right)^2} \ge 0.
    \end{array}\]

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