Question

\(\sqrt{x^2-1}+\sqrt{x^2-3x+2}=2\sqrt{x^2-4x+3}\)

 

Answer 1

\(\text{ĐK: }.......\Leftrightarrow x\le1\text{ hoặc }x\ge3\)

\(pt\Leftrightarrow\sqrt{\left(x-1\right)\left(x+1\right)}+\sqrt{\left(x-1\right)\left(x-2\right)}=2\sqrt{\left(x-1\right)\left(x-3\right)}\text{ (*)}\)

\(+TH1:x\le1\)

\(\left(\text{*}\right)\Leftrightarrow\sqrt{1-x}=0\text{ hoặc }\sqrt{-x-1}+\sqrt{2-x}=2\sqrt{3-x}\)

PT sau bình phương giải bình thường

\(+TH2:x\ge3\)

\(\left(\text{*}\right)\Leftrightarrow\sqrt{x+1}+\sqrt{x-2}=2\sqrt{x-3}\text{ (do }\sqrt{x-1}\ge\sqrt{3-1}>0\text{)}\)

bình phương giải bình thường.