Odpowiedź:
[tex]a)\\\\\sqrt{7+4\sqrt{3}}+\sqrt{12-6\sqrt{3}}=5\\\\\sqrt{(2+\sqrt{3})^2}+\sqrt{(3-\sqrt{3})^2}=5\\\\|2+\sqrt{3}|+|3-\sqrt{3}|=5\\\\2+\sqrt{3}+3-\sqrt{3}=5\\\\5=5\\\\L=P[/tex]
[tex]b)\\\\\sqrt{6-2\sqrt{5}}-\sqrt{9-4\sqrt{5}}=1\\\\\sqrt{(1-\sqrt{5})^2}-\sqrt{(2-\sqrt{5})^2}=1\\\\|1-\sqrt{5}|-|2-\sqrt{5}|\\\\-(1-\sqrt{5})-(-(2-\sqrt{5}))=1\\\\-1+\sqrt{5}-(-2+\sqrt{5})=1\\\\-1+\sqrt{5}+2-\sqrt{5}=1\\\\1=1\\\\L=P[/tex]
[tex]c)\\\\3\sqrt{11+6\sqrt{2}}-\sqrt{19-6\sqrt{2}}=10\\\\3\sqrt{(3+\sqrt{2})^2}-\sqrt{(1-3\sqrt{2})^2}=10\\\\3|3+\sqrt{2}|-|1-3\sqrt{2}|=10\\\\3(3+\sqrt{2})-(-(1-3\sqrt{2}))=10\\\\9+3\sqrt{2}-(-1+3\sqrt{2})=10\\\\9+3\sqrt{2}+1-3\sqrt{2}=10\\\\10=10\\\\L=P[/tex]
[tex]d)\\\\\sqrt{5+2\sqrt{6}}+\sqrt{5-2\sqrt{6}}=2\sqrt{3}\\\\\sqrt{(\sqrt{2}+\sqrt{3})^2}+\sqrt{(\sqrt{2}-\sqrt{3})^2}=2\sqrt{3}\\\\|\sqrt{2}+\sqrt{3}|+|\sqrt{2}-\sqrt{3}|=2\sqrt{3}\\\\\sqrt{2}+\sqrt{3}+(-(\sqrt{2}-\sqrt{3}))=2\sqrt{3}\\\\\sqrt{2}+\sqrt{3}+(-\sqrt{2}+\sqrt{3})=2\sqrt{3}\\\\\sqrt{2}+\sqrt{3}-\sqrt{2}+\sqrt{3}=2\sqrt{3}\\\\2\sqrt{3}=2\sqrt{3}\\\\L=P[/tex]
