Có A= \(x^4+5x^2-32\)
= \(\left(x^2\right)^2+2x^2.\frac{5}{2}+\frac{25}{4}-\frac{153}{4}\)
=\(\left(x^2+\frac{5}{2}\right)^2-\frac{153}{4}\)
Có \(\left(x^2+\frac{5}{2}\right)^2\) ≥ 0 ∀x
⇔\(\left(x^2+\frac{5}{2}\right)^2-\frac{153}{4}\ge-\frac{153}{4}\forall x\)
⇔A≥\(-\frac{153}{4}\)
Dấu "=" xảy ra khi: \(\left(x^2+\frac{5}{2}\right)^2=0\)
⇔\(x^2+\frac{5}{2}=0\)
⇔ \(x^2=-\frac{5}{2}\)(vô lí)
⇔\(x\in\varnothing\)
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\(\left\{{}\begin{matrix}x^4\ge0\\5x^2\ge0\end{matrix}\right.\) ;\(\forall x\)
\(\Rightarrow x^4+5x^2-32\ge-32\)
Dấu "=" xảy ra khi \(x=0\)