Toán Lớp 9: Tìm GTNN
√(x-2019) ² + √(x-2020) ²
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Toán Lớp 9: Tìm GTNN
√(x-2019) ² + √(x-2020) ²
Comments ( 1 )
\sqrt {{{\left( {x – 2019} \right)}^2}} + \sqrt {{{\left( {x – 2020} \right)}^2}} \\
= \left| {x – 2019} \right| + \left| {x – 2020} \right|\\
= \left| {x – 2019} \right| + \left| {2020 – x} \right|\\
\ge \left| {x – 2019 + 2020 – x} \right|\\
\Leftrightarrow \sqrt {{{\left( {x – 2019} \right)}^2}} + \sqrt {{{\left( {x – 2020} \right)}^2}} \ge 1\\
\Leftrightarrow GTNN = 1\\
Khi:2019 \le x \le 2020
\end{array}$