[latex] \frac{ \sqrt{2} - 1 }{ \sqrt{2} +1} [/latex]=[latex] \sqrt[3]{ \frac{10-7 \sqrt{2} }{10+ 7 \sqrt{2} } } [/latex] доказать справедливость

[latex]\sqrt[3]{\frac{10-7\sqrt{2}}{10+7\sqrt{2}}}:\frac{\sqrt{2}-1}{\sqrt{2}+1} = \sqrt[3]{\frac{10-7\sqrt{2}}{10+7\sqrt{2}}}\cdot\frac{\sqrt{2}+1}{\sqrt{2}-1} = \sqrt[3]{\frac{10-7\sqrt{2}}{10+7\sqrt{2}}\cdot(\frac{\sqrt{2}+1}{\sqrt{2}-1})^3} =\\= \sqrt[3]{\frac{10-7\sqrt{2}}{10+7\sqrt{2}}\cdot\frac{2\sqrt{2}+6+3\sqrt{2}+1}{2\sqrt{2}-6+3\sqrt{2}-1}} = \sqrt[3]{\frac{(10-7\sqrt{2})(5\sqrt{2}+7)}{(10+7\sqrt{2})(5\sqrt{2}-7)}} =[/latex] [latex]=\sqrt[3]{\frac{50\sqrt{2}+70-70-49\sqrt{2}}{50\sqrt{2}-70+70-49\sqrt{2}}} = \sqrt[3]{\frac{\sqrt{2}}{\sqrt{2}}} = \sqrt[3]{1} = 1.[/latex]