\(\sqrt{17-6.\sqrt{2+\sqrt{8+2.2\sqrt{2}+1}}}+1^2\)
\(=\sqrt{17-6\sqrt{2+\sqrt{\left(2\sqrt{2}+1\right)^2}}}+1\)
\(=\sqrt{17-6\sqrt{2+2\sqrt{2}+1}}+1\)
\(=\sqrt{17-6\sqrt{\left(\sqrt{2}+1\right)^2}}+1\)
\(=\sqrt{17-6\left(\sqrt{2}+1\right)}+1=\sqrt{17-6\sqrt{2}-6}+1\)
\(=\sqrt{11-6\sqrt{2}}+1=\sqrt{\left(3-\sqrt{2}\right)^2}+1=3-\sqrt{2}+1=4-\sqrt{2}\)
Đề như thế này mới đúng nè:
\(\sqrt{17-6\sqrt{2+\sqrt{9+4\sqrt{2}}}}\)
= \(\sqrt{17-6\sqrt{2+\sqrt{8+2.2.\sqrt{2}+1}}}\)
= \(\sqrt{17-6\sqrt{2+\sqrt{\left(\sqrt{8}+1\right)^2}}}\)
=\(\sqrt{17-6\sqrt{2+\sqrt{8}+1}}\)
= \(\sqrt{17-6\sqrt{2+\sqrt{4}.\sqrt{2}+1}}\)
= \(\sqrt{17-6\sqrt{2+2.\sqrt{2}+1}}\)
= \(\sqrt{17-6\sqrt{\left(\sqrt{2}+1\right)^2}}\)
= \(\sqrt{17-6\left(\sqrt{2}+1\right)}\)
= \(\sqrt{17-6\sqrt{2}-6}\)
= \(\sqrt{11-6\sqrt{2}}\)
= \(\sqrt{9-2.3.\sqrt{2}+2}\)
= \(\sqrt{\left(3-\sqrt{2}\right)^2}\)
= \(3-\sqrt{2}\)
Bà chị chưa làm xong toán thầy ak???
