Đặt \(A=\sqrt{17-3\sqrt{32}+\sqrt{17+3\sqrt{32}}}\)
\(\Rightarrow\sqrt{2}.A=\sqrt{34-6\sqrt{32}+2\sqrt{17+3\sqrt{32}}}\)
\(\Leftrightarrow\sqrt{2}.A=\sqrt{34-6\sqrt{32}+\sqrt{68+12\sqrt{32}}}\)
\(\Leftrightarrow\sqrt{2}.A=\sqrt{34-6\sqrt{32}+\sqrt{\left(\sqrt{32}+6\right)^2}}\)
\(\Leftrightarrow\sqrt{2}.A=\sqrt{34-6\sqrt{32}+\left|\sqrt{32}+6\right|}\)
\(\Leftrightarrow\sqrt{2}.A=\sqrt{34-6\sqrt{32}+\sqrt{32}+6}\)
\(\Leftrightarrow\sqrt{2}.A=\sqrt{40-5\sqrt{32}}\)
\(\Leftrightarrow\sqrt{2}.A=\sqrt{40-20\sqrt{2}}\)
\(\Leftrightarrow A=\dfrac{\sqrt{40-20\sqrt{2}}}{\sqrt{2}}\)
\(\Leftrightarrow A=\sqrt{\dfrac{40-20\sqrt{2}}{2}}\)
\(\Leftrightarrow A=\sqrt{\dfrac{40}{2}-\dfrac{20\sqrt{2}}{2}}\)
\(\Leftrightarrow A=\sqrt{20-10\sqrt{2}}\)
