Question

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

Answer 1

\(\Leftrightarrow\sqrt{\left(x+1\right)+2\sqrt{x+1}+1}\)+\(\sqrt{\left(x+1\right)-2\sqrt{x+1}+1}\)=1+x

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

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

\(\Leftrightarrow2\sqrt{x+1}=1+x\)

\(\Leftrightarrow2\sqrt{x+1}=\left(\sqrt{x+1}\right)^2\)

\(\Leftrightarrow2=\sqrt{x+1}\)

\(\Leftrightarrow x+1=4\)

\(\Leftrightarrow x=3\)

Vậy x = 3.