Question

Giải phương trình sau

2 /x-1/= x² -2x -2

Answer 1

Nếu \(x-1\ge0\)=>\(x\ge1\)

PT\(\Leftrightarrow2\left(x-1\right)=x^2-2x-2\)

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

\(\Leftrightarrow x\left(x-4\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(loai\right)\\x=4\left(tm\right)\end{matrix}\right.\)

Nếu x-1<0=>x<1

\(PT\Leftrightarrow2\left(1-x\right)=x^2-2x-2\)

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

\(\Leftrightarrow\left(x-2\right)\left(x+2\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2\left(loai\right)\\x=-2\left(tm\right)\end{matrix}\right.\)