Question

Tìm GTNN :

4𝑥^4+12𝑥^2+11

Answer 1

Đặt \(A=4x^4+12x^2+11\)

Ta có \(\left\{{}\begin{matrix}x^4\ge0\\x^2\ge0\end{matrix}\right.\) ; \(\forall x\)

\(\Rightarrow4x^4+12x^2\ge0;\forall x\)

\(\Rightarrow4x^4+12x^2+11\ge11;\forall x\)

\(\Rightarrow A_{min}=11\) khi \(x=0\)

Answer 2

Ta có: \(4x^4\ge0\forall x\)

\(12x^2\ge0\forall x\)

Do đó: \(4x^4+12x^2\ge0\forall x\)

\(\Leftrightarrow4x^4+12x^2+11\ge11\forall x\)

Dấu '=' xảy ra khi x=0