Réponse :
salut
1)
[tex]\frac{\sqrt{3}-\sqrt{2} }{\sqrt{3}+\sqrt{2} } =\frac{(\sqrt{3}-\sqrt{2})(\sqrt{3}-\sqrt{2})}{(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})} } \\\\\frac{\sqrt{3}-\sqrt{2} }{\sqrt{3}+\sqrt{2} } =\frac{3-2\sqrt{6}+2 }{3-2}=5-2\sqrt{6} \\[/tex]
2)
i)
on a (√5 +√7)²=(√5)²+2√5×√7+(√7)²
=5+2√35+7
=12+2√35
et [√(12+2√35)]²=12+2√35
donc √5 +√7=√(12+2√35)
ii)
on a (1+√2)²=1+2√2+2=3+2√2
et [√(1+√2)/√(√2-1) ]²=(1+√2)/(√2-1)
=(1+√2)(√2+1)/(√2-1)(√2+1)
=(1+2√2+2)/(2-1)
=3+2√2
donc 1+√2=√(1+√2)/√(√2-1)
