\(A=\frac{2x+3y}{2x+y+2}\)

\(\Leftrightarrow A\left(2x+y+2\right)=2x+3y\)

\(\Leftrightarrow2A=2x\left(1-A\right)+y\left(3-A\right)\)

\(\Leftrightarrow\left(2A\right)^2=\left(2x\left(1-A\right)+y\left(3-A\right)\right)^2\le\left(4x^2+y^2\right)\left(\left(1-A\right)^2+\left(3-A\right)^2\right)\)

\(\Leftrightarrow\left(2A\right)^2\le\left(\left(1-A\right)^2+\left(3-A\right)^2\right)\)

\(\Leftrightarrow-5\le A\le1\)

Chết em ấn nhầm nút rồi

\(x^2+4x-6=\left(x+2\right)^2-10\ge0-10=-10\Rightarrow A_{min}=-10\Leftrightarrow x=-2\) 

\(B=|2x-1|+|7-2x|-10\ge|2x-1+7-2x|-10=6-10=-4.\Rightarrow B_{min}=-4\Leftrightarrow\frac{1}{2}\le x\le\frac{7}{2}\)

1/ \(x^2-2x+7\)

\(=x^2-\frac{1}{2}\cdot2x+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2+7\)

\(=x^2-\frac{1}{2}\cdot2x+\left(\frac{1}{2}\right)^2-\frac{1}{4}+7\)

\(=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}+7\)

\(=\left(x-\frac{1}{2}\right)^2+\frac{27}{4}\)

Có  \(\left(x-\frac{1}{2}\right)^2\ge0\Rightarrow\left(x-\frac{1}{2}\right)^2+\frac{27}{4}\ge\frac{27}{4}\)

\(\Rightarrow GTNNx^2-2x+7=\frac{27}{4}\)

               với  \(\left(x-\frac{1}{2}\right)^2=0;x=\frac{1}{2}\)

2/ \(4x^2+2x+9\)

\(=\left(2x\right)^2+2\cdot2\cdot\frac{1}{2}x+\left(\frac{1}{2}\right)^2-\left(\frac{1}{2}\right)^2+9\)

\(=\left(2x+\frac{1}{2}\right)^2-\frac{1}{4}+9\)

\(=\left(2x+\frac{1}{2}\right)^2+\frac{35}{4}\)

có \(\left(2x+\frac{1}{2}\right)^2\ge0\Rightarrow\left(2x+\frac{1}{2}\right)^2+\frac{35}{4}\ge\frac{35}{4}\)

\(\Rightarrow GTNN4x^2+2x+9=\frac{35}{4}\)

                với  \(\left(2x+\frac{1}{2}\right)^2=0;x=-\frac{1}{4}\)

đặt các biểu thức trên bằng a rồi nhân lên dùng denta