Question

Tìm x:

\(\sqrt{x+\sqrt{x+\frac{1}{2}+\sqrt{x+\frac{1}{4}}}}=2\)

Answer 1

ĐKXĐ: ...

\(\Leftrightarrow\sqrt{x+\sqrt{x+\frac{1}{4}+\sqrt{x+\frac{1}{4}}+\frac{1}{4}}}=2\)

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

\(\Leftrightarrow\sqrt{x+\sqrt{x+\frac{1}{4}}+\frac{1}{2}}=2\)

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

\(\Leftrightarrow\sqrt{x+\frac{1}{4}}+\frac{1}{2}=2\)

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

\(\Rightarrow x=2\)