Đáp án:
$\left\{\begin{matrix}
x=\frac{60+6\sqrt{205}}{7}\\
x=\frac{60-6\sqrt{205}}{7}
\end{matrix}\right.$
Giải thích các bước giải:
$\begin{array}{l}\frac{x^{2}+81x^{2}}{(x+9)^{2}}=40(ĐK:x\neq -9)\\\Leftrightarrow \frac{82x^{2}}{(x+9)^{2}}=40\\\Leftrightarrow 82x^{2}=40(x+9)^{2}\\\Leftrightarrow 41x^{2}=20(x+9)^{2}\\\Leftrightarrow 41x^{2}-20(x+9)^{2}=0\\\Leftrightarrow 41x^{2}-20(x^{2}+18x+81)=0\\\Leftrightarrow 41x^{2}-20x^{2}-360x-1620=0\\\Leftrightarrow 21x^{2}-360x-1620=0\\\Leftrightarrow 7x^{2}-120x-540=0\\\Leftrightarrow x=\frac{-(-120)±\sqrt{(-120)^{2}-4.7.(-540)}}{2.7}\\\Leftrightarrow x=\frac{120±\sqrt{14400+15120}}{14}\\\Leftrightarrow x=\frac{120±\sqrt{29520}}{14}\\\Leftrightarrow x=\frac{120±12\sqrt{205}}{14}\\\Leftrightarrow \left\{\begin{matrix}
x=\frac{120±12\sqrt{205}}{14}\\
x=\frac{120-12\sqrt{205}}{14}
\end{matrix}\right.\\\Leftrightarrow \left\{\begin{matrix}
x=\frac{60±6\sqrt{205}}{7}\\
x=\frac{60-6\sqrt{205}}{7}
\end{matrix}\right.\\\Leftrightarrow \left\{\begin{matrix}
x=\frac{60+6\sqrt{205}}{7}\\
x=\frac{60-6\sqrt{205}}{7}
\end{matrix}\right.\end{array}$
