Giải thích các bước giải:
\(\begin{array}{l}
1)A = 2{x^2} + 15x + 18 - {x^2} - 7x - 10 + 10\\
= {x^2} + 8x + 18\\
B = 2{x^2} + 4x - \left( {{x^2} + 2x - 3} \right)\\
= {x^2} + 2x + 3\\
2)\,A = {x^2} + 8x + 16 + 2 = {\left( {x + 4} \right)^2} + 2 > 0\\
B = {x^2} + 2x + 1 + 2 = {\left( {x + 1} \right)^2} + 2 > 0\\
3)\,Thay\,x = \dfrac{2}{3}\,vao\,A\,ta\,co\\
A = {\left( {\dfrac{2}{3}} \right)^2} + 8.\dfrac{2}{3} + 18 = \dfrac{{214}}{9}\\
4)\,{A_{\min }} = 2 \Leftrightarrow x = - 4\\
{B_{\min }} = 2 \Leftrightarrow x = - 1
\end{array}\)