Question

$frac{ sqrt{2} - 1 }{ sqrt{2} +1}$=$sqrt[3]{ frac{10-7 sqrt{2} }{10+ 7 sqrt{2} } }$

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Answer 1

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