\(A=x^4-7x^2\)
\(=\left(x^4-7x^2+\dfrac{49}{4}\right)-\dfrac{49}{4}\)
\(=\left[\left(x^2\right)^2-2.x^2.\dfrac{7}{2}+\left(\dfrac{7}{2}\right)^2\right]-\dfrac{49}{4}\)
\(=\left(x^2-\dfrac{7}{2}\right)^2-\dfrac{49}{4}\ge-\dfrac{49}{4}\)
Dấu = xảy ra \(\Leftrightarrow x^2-\dfrac{7}{2}=0\Leftrightarrow x^2=\dfrac{7}{2}\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)
Vậy \(Min_A=-\dfrac{49}{4}\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{7}{2}\\x=-\dfrac{7}{2}\end{matrix}\right.\)
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