Question

Giải phương trình: \(\frac{x^2}{4}+\frac{900}{x^2}=2+48(\frac{10}{x}-\frac{x}{6})\)

Answer 1

ĐKXĐ: ...

Đặt \(\frac{10}{x}-\frac{x}{6}=a\Rightarrow a^2=\frac{100}{x^2}+\frac{x^2}{36}-\frac{10}{3}\Rightarrow\frac{100}{x^2}+\frac{x^2}{36}=a^2+\frac{10}{3}\)

\(\Rightarrow\frac{900}{x^2}+\frac{x^2}{4}=9a^2+30\)

Phương trình trở thành:

\(9a^2+30=2+48a\)

\(\Leftrightarrow9a^2-48a+28=0\Rightarrow\left[{}\begin{matrix}a=\frac{14}{3}\\a=\frac{2}{3}\end{matrix}\right.\)

\(\Rightarrow\left[{}\begin{matrix}\frac{10}{x}-\frac{x}{6}=\frac{14}{3}\\\frac{10}{x}-\frac{x}{6}=\frac{2}{3}\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}\frac{x^2}{6}+\frac{14}{3}x-10=0\\\frac{x^2}{6}+\frac{2}{3}x-10=0\end{matrix}\right.\)