Question

giải pt sau

/x+1/ + /x-1/=4

Answer 1

+) Xét \(x\ge1\) có:

\(x+1+x-1=4\)

\(\Leftrightarrow2x=4\Leftrightarrow x=2\) ( t/m )

+) Xét \(-1\le x< 1\) ta có:

\(x+1+1-x=4\)

\(\Leftrightarrow2=4\) ( vô lí )

+) Xét \(x< -1\) có:
\(-x-1+1-x=4\)

\(\Leftrightarrow-2x=4\)

\(\Leftrightarrow x=-2\) ( t/m )

Vậy x = 2 hoặc x = -2

Answer 2

xét trường hợp : TH₁: \(x\ge1\)

\(\Rightarrow\) \(\left|x+1\right|+\left|x-1\right|\) \(\Leftrightarrow\) \(x+1+x-1=4\) \(\Leftrightarrow\) \(2x=4\) \(\Leftrightarrow\) \(x=2\)

TH₂ : \(x\le-1\)

\(\Rightarrow\) \(\left|x+1\right|+\left|x-1\right|\) \(\Leftrightarrow\) \(-x-1+1-x=4\) \(\Leftrightarrow\) \(-2x=4\) \(\Leftrightarrow\) \(x=-2\)

vậy : \(x=-2;x=2\)