Question

Giải phương trình :

\(\sqrt{2x-2+2\sqrt{2x-3}}+\sqrt{2x+13+8\sqrt{2x-3}}=5\)

Answer 1

ĐKXĐ: \(x\ge\frac{3}{2}\)

\(\sqrt{2x-3+2\sqrt{2x-3}+1}+\sqrt{2x-3+8\sqrt{2x-3}+16}=5\)

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

\(\Leftrightarrow\left|\sqrt{2x-3}+1\right|+\left|\sqrt{2x-3}+4\right|=5\)

\(\Leftrightarrow\sqrt{2x-3}+1+\sqrt{2x-3}+4=5\)

\(\Leftrightarrow2\sqrt{2x-3}=0\)

\(\Rightarrow2x-3=0\Rightarrow x=\frac{3}{2}\)