Ta giải như sau:
\(A=\sqrt{1+2\sqrt{6}+6}-\sqrt{1-2\sqrt{6}+6}\)
\(=\sqrt{\left(1+\sqrt{6}\right)^2}-\sqrt{\left(1-\sqrt{6}\right)^2}\)
\(=1+\sqrt{6}+1-\sqrt{6}\)
\(=2\)
\(B^2=2+\sqrt{2+\sqrt{2+\sqrt{2+...}}}=2+B\)
\(\Leftrightarrow B^2-B-2=0\)
\(\Leftrightarrow\left(B+1\right)\left(B-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}B=-1\\B=2\end{cases}}\)Ta lấy B=2 vì B>0
\(C=\sqrt{2\sqrt{2\sqrt{2...}}}\)
\(\Rightarrow C^2=2\sqrt{2\sqrt{2\sqrt{2...}}}=2C\)
\(\Leftrightarrow C^2-2C=0\)
\(\Leftrightarrow C\left(C-2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}C=0\\C=2\end{cases}}\)Ta lấy C=2 vì C>0
Ok r bn nhó ^^
