Question

Arată că(radical3+radical7-radical11)(radical3+radical7+radical11)+(radical3-radical7)^2 este un număr rațional

Answer 1

$(\sqrt{3}+\sqrt{7}-\sqrt{11})(\sqrt{3}+\sqrt{7}+\sqrt{11})+(\sqrt{3}-\sqrt{7})^{2}=\\=(\sqrt{3}+\sqrt{7})^2-\sqrt{11}^2+(\sqrt{3}-\sqrt{7})^{2}=\\=3+2\sqrt{21}+7-11+3-2\sqrt{21}+7=9$∈Q