Toán Lớp 8: tìm GTNN của A= x^4 -6x^3 +13x^2 -12x +2021
Giúp e vs ạ ai lm hộ cái
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Toán Lớp 8: tìm GTNN của A= x^4 -6x^3 +13x^2 -12x +2021
Giúp e vs ạ ai lm hộ cái
Comments ( 2 )
\quad A = x^4 – 6x^3 +13x^2 -12x +2021\\
\to A = (x^4 – 6x^3 + 9x^2) + (4x^2 -12x) + 2021\\
\to A = (x^2 – 3x)^2 + 4(x^2 – 3x) + 2021\\
\to A = (x^2 – 3x + 2)^2 + 2017\\
\text{Ta có:}\\
\quad (x^2 – 3x + 2)^2\geqslant 0\quad \forall x\\
\Leftrightarrow (x^2 – 3x + 2)^2 + 2017\geqslant 2017\\
\Leftrightarrow A\geqslant 2017\\
\text{Dấu = xảy ra khi và chỉ khi}\\
\quad x^2 -3x + 2 =0\\
\Leftrightarrow (x-1)(x-2) = 0\\
\Leftrightarrow \left[\begin{array}{l}x = 1\\x = 2\end{array}\right.\\
\text{Vậy}\ \min A = 2017\Leftrightarrow x\in \{1;2\}
\end{array}\)