Odpowiedź:
[tex]a)\ \ (\sqrt{7+\sqrt{6}}+\sqrt{7-\sqrt{6}})^2=(\sqrt{7+\sqrt{6}})^2+2\sqrt{7+\sqrt{6}}\cdot\sqrt{7-\sqrt{6}}+(\sqrt{7-\sqrt{6}})^2=\\=7+\sqrt{6}+2\sqrt{(7+\sqrt{6})(7-\sqrt{6})}+7-\sqrt{6}=7+2\sqrt{7^2-(\sqrt{6})^2}+7=\\\\=7+2\sqrt{49-6}+7=14+2\sqrt{43}[/tex]
[tex]b)\ \ (\sqrt{11-\sqrt{7}}-\sqrt{11+\sqrt{7}})^2=\\\\=(\sqrt{11-\sqrt{7}})^2-2\sqrt{11-\sqrt{7}}\cdot\sqrt{11+\sqrt{7}}+(\sqrt{11+\sqrt{7}})^2=\\\\=11-\sqrt{7}-2\sqrt{(11-\sqrt{7})(11+\sqrt{7})}+11+\sqrt{7}=11-2\sqrt{11^2-(\sqrt{7})^2}+11=\\\\=22-2\sqrt{121-7}=22-2\sqrt{114}[/tex]
