\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}+2\sqrt{x}+1+2\left(\sqrt{x}+1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=\sqrt{x}\left(\sqrt{x}-1\right)+2\sqrt{x}+1+2\left(\sqrt{x}+1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=x-3\sqrt{x}+2\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=\left(\sqrt{x}-\dfrac{3}{2}\right)^2-\dfrac{1}{4}\end{matrix}\right.\)
\(A\ge-\dfrac{1}{4}\)
tai x =9/4
\(A=\dfrac{x^2-\sqrt{x}}{x+\sqrt{x}+1}+\dfrac{2x+\sqrt{x}}{\sqrt{x}}+\dfrac{2\left(x-1\right)}{\sqrt{x}-1}\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=\sqrt{x}\left(\sqrt{x}-1\right)+2\sqrt{x}+1+2\left(\sqrt{x}+1\right)\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=x+3\sqrt{x}+3\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x>0;x\ne1\\A=\left(\sqrt{x}+\dfrac{3}{2}\right)^2+\dfrac{3}{4}\end{matrix}\right.\)
KL:
Không có GT NN
