Question

Giải phương trình : \(\dfrac{1}{x^2}+\dfrac{1}{x^2+1}=\dfrac{9}{2\left(x^2+2\right)}\)

Answer 1

ĐKXĐ: \(x\ne0\).

\(PT\Leftrightarrow\dfrac{2x^2+1}{x^2\left(x^2+1\right)}=\dfrac{9}{2\left(x^2+2\right)}\)

\(\Rightarrow2\left(x^2+2\right)\left(2x^2+1\right)=9x^2\left(x^2+1\right)\)

\(\Leftrightarrow5x^4-x^2-4=0\Leftrightarrow\left(x^2-1\right)\left(5x^2+4\right)=0\)

\(\Leftrightarrow x^2=1\Leftrightarrow x=\pm1\) (TMĐK)

Vậy..