Question

Giải phương trình : \(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}=2\)

Answer 1

\(< =>\left(\sqrt{x+2\sqrt{x-1}}+\sqrt{x-2\sqrt{x-1}}\right)^2=4\)

\(< =>x+2\sqrt{x-1}+2\left(\sqrt{x+2\sqrt{x-1}}\right).\left(\sqrt{x-2\sqrt{x-1}}\right)+x-2\sqrt{x-1}=4\)

\(< =>2x+2\sqrt{\left(x+2\sqrt{x-1}\right).\left(x-2\sqrt{x-1}\right)}=4\)

\(< =>2x+\sqrt{x^2-4\left(x-1\right)}=4\)

\(< =>2x+\sqrt{x^2-4x+4}=4\)

\(< =>2x+2.\sqrt{\left(x-2\right)^2}=4\)

\(< =>2\left|x-2\right|=4-2x=2\left(2-x\right)\)

\(< =>\left|x-2\right|=2-x=>x-2< 0=>x< 2\)