Question

Answer 1

d) \(\sqrt{x-1}-\sqrt{x+1}=2\)

\(\sqrt{x-1}=2+\sqrt{x+1}\left(đk:x\ge1\right)\)

\(x-1=5+x+4\sqrt{x+1}\)

\(-6=\sqrt{x+1}\left(\text{vô lý}\right)\)

Vậy phương trình vô nghiệm

Answer 2

e) \(\sqrt{x-1-2\sqrt{x-1}+1}-\sqrt{x-1}=1\)

\(\sqrt{\left(\sqrt{x-1}-1\right)^2}-\sqrt{x-1}=1\left(đk:x\ge1\right)\)

\(\sqrt{x-1}-1-\sqrt{x-1}=1\)

\(-1=1\left(\text{vô lý}\right)\)

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Answer 3

e) 

\(\sqrt{x-2\sqrt{x-1}}-\sqrt{x-1}=1\)

<=>\(x-2\sqrt{x-1}=x +2\sqrt{x+1}\)

<=>\(-2\sqrt{x-1}=2\sqrt{x+1}\)(loai)

Vi \(\sqrt{A}\ge0\)