Question

Giải phương trình

\(\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4-2\sqrt{2x-5}}=4\)

Answer 1

ĐKXĐ: \(x\ge\dfrac{5}{2}\)

\(\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4-2\sqrt{2x-5}}=4\)

\(\Leftrightarrow\sqrt{\left(2x-5\right)+2.\sqrt{2x-5}\cdot3+9}+\sqrt{\left(2x-5\right)-2\sqrt{2x-5}.1+1}=4\)\(\Leftrightarrow\sqrt{\left(2x-5+3\right)^2}+\sqrt{\left(2x-5-1\right)^2}=4\)

\(\Leftrightarrow\left|2x-2\right|+\left|2x-6\right|=4\)

\(\Leftrightarrow\left|x-1\right|+\left|x-3\right|=4\)

Xét x<1:

=>1-x+3-x=4

=>-2x=0

=>x=0

Xét \(1\le x< 3\)

=>x-1+3-x=4

=>0x=2(vô lý)

Xét \(x\ge3\)

=>x-1+x-3=4

=>2x=-2

=>x=-1