Toán Lớp 8: tìm GTNN của
a=x^2-6x+209
b=x^2+y^2+2y+2026
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Toán Lớp 8: tìm GTNN của
a=x^2-6x+209
b=x^2+y^2+2y+2026
Comments ( 1 )
A = {x^2} – 6x + 209\\
= {x^2} – 6x + 9 + 200\\
= {\left( {x – 3} \right)^2} + 200\\
Do:{\left( {x – 3} \right)^2} \ge 0\\
\Leftrightarrow {\left( {x – 3} \right)^2} + 200 \ge 200\\
\Leftrightarrow A \ge 200\\
\Leftrightarrow GTNN:A = 200\,khi:x = 3\\
B = {x^2} + {y^2} + 2y + 2026\\
= {x^2} + {y^2} + 2y + 1 + 2025\\
= {x^2} + {\left( {y + 1} \right)^2} + 2025 \ge 2025\\
\Leftrightarrow B \ge 2025\\
\Leftrightarrow GTNN:B = 2025\,khi:\left\{ \begin{array}{l}
x = 0\\
y = – 1
\end{array} \right.
\end{array}$