\(A=\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}\)
\(A=\sqrt{x-1-2\sqrt{x-1}+1}+\sqrt{x-1+2\sqrt{x-1}+1}\)
\(A=\sqrt{\left(\sqrt{x-1}-1\right)^2}+\sqrt{\left(\sqrt{x-1}+1\right)^2}\)
\(A=\left|\sqrt{x-1}-1\right|+\left|\sqrt{x-1}+1\right|\)
\(A=\left|1-\sqrt{x-1}\right|+\left|\sqrt{x-1}+1\right|\ge\left|1-\sqrt{x-1}+\sqrt{x-1}+1\right|=\left|2\right|=2\)
Dấu "=" xảy ra \(\Leftrightarrow1\le x\le2\)
\(B=\sqrt{x^2+4x+4}+\sqrt{x^2+6x+9}\)
\(B=\sqrt{\left(x+2\right)^2}+\sqrt{\left(x+3\right)^2}\)
\(B=\left|x+2\right|+\left|x+3\right|\)
\(B=\left|-x-2\right|+\left|x+3\right|\ge\left|-x-2+x+3\right|=\left|1\right|=1\)
Dấu "=" xảy ra \(\Leftrightarrow-3\le x\le-2\)
