Question

giải phương trình:

 11/x² - 25/(x+5)² = 1

giải giúp em với ạ!

Answer 1

ĐKXĐ: \(x\ne\left\{0;-5\right\}\)

\(\Leftrightarrow\dfrac{11}{x^2}-\left[1-\dfrac{10}{x+5}+\left(\dfrac{5}{x+5}\right)^2+\dfrac{10}{x+5}\right]=0\)

\(\Leftrightarrow\dfrac{11}{x^2}-\left[\left(1-\dfrac{5}{x+5}\right)^2+\dfrac{10}{x+5}\right]=0\)

\(\Leftrightarrow\dfrac{11}{x^2}-\dfrac{10}{x+5}-\left(\dfrac{x}{x+5}\right)^2=0\)

\(\Leftrightarrow\left(\dfrac{1}{x}-\dfrac{x}{x+5}\right)\left(\dfrac{11}{x}+\dfrac{x}{x+5}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{1}{x}-\dfrac{x}{x+5}=0\\\dfrac{11}{x}+\dfrac{x}{x+5}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-x-5=0\\x^2+11x+55=0\end{matrix}\right.\)

\(\Leftrightarrow...\) (bấm máy)