Question

Giải phương trình

x - 2/x + 2 — x + 2/x - 2 = 24/4 - x²

Answer 1

ĐKXĐ: \(x\ne\pm2\)

Ta có: \(\frac{x-2}{x+2}-\frac{x+2}{x-2}=\frac{24}{4-x^2}\)

\(\Leftrightarrow\frac{x-2}{x+2}-\frac{x+2}{x-2}=\frac{-24}{x^2-4}\)

\(\Leftrightarrow\frac{\left(x-2\right)^2}{\left(x+2\right)\left(x-2\right)}-\frac{\left(x+2\right)^2}{\left(x+2\right)\left(x-2\right)}=\frac{-24}{\left(x-2\right)\left(x+2\right)}\)

Suy ra: \(x^2-4x+4-\left(x^2+4x+4\right)=-24\)

\(\Leftrightarrow x^2-4x+4-x^2-4x-4+24=0\)

\(\Leftrightarrow24-8x=0\)

\(\Leftrightarrow8x=24\)

hay x=3(tm)

Vậy: Tập nghiệm S={3}