Question

Tìm x:

1/(2*(x-1)) + 3/(x^2 -2) = 1/4

Answer 1

\(\left[2.\left(x-1\right)\right]+\dfrac{3}{x^2-2}=\dfrac{1}{4}\)

\(\Leftrightarrow2x-2+\dfrac{3}{x^2-2}-\dfrac{1}{4}=0\)\(\left(dkxd:x\ne\pm\sqrt{2}\right)\)

\(\Leftrightarrow4\left(2x-2\right)\left(x^2-2\right)-\left(x^2-2\right)=0\)

\(\Leftrightarrow\left(x^2-2\right)\left[4\left(2x-2\right)-1\right]=0\)

\(\Leftrightarrow\left(x^2-2\right)\left(8x-9\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2-2=0\\8x-9=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\pm\sqrt{2}\left(ktmdk\right)\\x=\dfrac{9}{8}\left(tmdk\right)\end{matrix}\right.\)

Vậy \(S=\left\{\dfrac{9}{8}\right\}\)