Bonjour,
1)
[tex]a^{2} =(\sqrt{5} -\sqrt{2} )^{2} \\\\=(\sqrt{5})^{2} -2*\sqrt{5}*\sqrt{2}+(\sqrt{2})^{2}\\\\=5-2*\sqrt{5*2} +2\\\\=7-2\sqrt{10}[/tex]
[tex]b^{2} =(5+\sqrt{2})^{2} \\\\=5^{2} +2*5*\sqrt{2}+(\sqrt{2})^{2} \\\\=25 + 10\sqrt{2} +2 \\\\=27+10\sqrt{2}[/tex]
2)
[tex]a^{2} +b^{2} =(7-2\sqrt{10}) + (27+10\sqrt{2}) \\\\=7-2\sqrt{10}+27+10\sqrt{2} \\\\=34-2\sqrt{10} +10\sqrt{2}[/tex]
[tex]\sqrt{a^{2}+b^{2}} =\sqrt{ 7-2\sqrt{10}+27+10\sqrt{2}}\\\\=\sqrt{34-2\sqrt{10}+10\sqrt{2} }\\\\=\sqrt{2(17 +5\sqrt{2}-\sqrt{10}) }[/tex]
