Toán Lớp 8: Tìm GTNN của biểu thức A=-5/2x^2-4x+4
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Toán Lớp 8: Tìm GTNN của biểu thức A=-5/2x^2-4x+4
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A = – \dfrac{5}{{2{x^2} – 4x + 4}}\\
= – \dfrac{5}{{2\left( {{x^2} – 2x + 2} \right)}}\\
= – \dfrac{5}{{2\left( {{x^2} – 2x + 1 + 1} \right)}}\\
= – \dfrac{5}{{2{{\left( {x – 1} \right)}^2} + 2}}\\
Do:2{\left( {x – 1} \right)^2} \ge 0\forall x\\
\to 2{\left( {x – 1} \right)^2} + 2 \ge 2\\
\to \dfrac{5}{{2{{\left( {x – 1} \right)}^2} + 2}} \le \dfrac{5}{2}\\
\to – \dfrac{5}{{2{{\left( {x – 1} \right)}^2} + 2}} \ge – \dfrac{5}{2}\\
\to Min = – \dfrac{5}{2}\\
\Leftrightarrow x – 1 = 0\\
\to x = 1
\end{array}\)