Đáp án:
$\begin{array}{l}
a){\left( {7 + 2x} \right)^2} + {\left( {x - 7} \right)^2} - 9 = 2\left( {7 + 2x} \right)\left( {x - 7} \right)\\
\Leftrightarrow 49 + 28x + 4{x^2} + {x^2} - 14x + 49 - 9\\
= 2.\left( {7x - 49 + 2{x^2} - 14x} \right)\\
\Leftrightarrow 5{x^2} + 14x + 89 = 4{x^2} - 14x - 98\\
\Leftrightarrow {x^2} + 28x + 187 = 0\\
\Leftrightarrow {x^2} + 11x + 17x + 187 = 0\\
\Leftrightarrow \left( {x + 11} \right)\left( {x + 17} \right) = 0\\
\Leftrightarrow x = - 11;x = - 17\\
Vậy\,x = - 11;x = - 17\\
b){\left( {x + 2} \right)^2} - {x^3} + 6{x^2} = 7\\
\Leftrightarrow {x^2} + 4x + 4 - {x^3} + 6{x^2} = 7\\
\Leftrightarrow {x^3} - 7{x^2} - 4x + 3 = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x = - 0,91\\
x = 0,43\\
x = 7,48
\end{array} \right.\\
Vậy\,x = - 0,91;x = 0,43;x = 7,48
\end{array}$
