Question

Tìm x:

\(\dfrac{2}{x-\sqrt{x^2-4}}+\dfrac{2}{x+\sqrt{x^2-4}}=5\)

Answer 1

ĐK: \(x\ge2;x\le-2\)

\(\dfrac{2}{x-\sqrt{x^2-4}}+\dfrac{2}{x+\sqrt{x^2-4}}=5\)

\(\Leftrightarrow\dfrac{2\left(x+\sqrt{x^2-4}\right)}{x^2-x^2+4}+\dfrac{2\left(x-\sqrt{x^2-4}\right)}{x^2-x^2+4}=5\)

\(\Leftrightarrow x+\sqrt{x^2-4}+x-\sqrt{x^2-4}=10\)

\(\Leftrightarrow2x=10\)

\(\Leftrightarrow x=5\left(tm\right)\)