Bonjour ;
Exercice n° 134 .
On a :
[tex]\sqrt{18} =\sqrt{2\times9}=\sqrt{2}\times\sqrt{9}=3\sqrt{2}\ .[/tex]
[tex]E=\dfrac{5}{\sqrt{2}+\sqrt{18}} +\dfrac{3}{\sqrt{2}-\sqrt{18}}=\dfrac{5}{\sqrt{2}+3\sqrt{2}} +\dfrac{3}{\sqrt{2}-3\sqrt{2}}\\\\\\=\dfrac{5}{4\sqrt{2}} +\dfrac{3}{-2\sqrt{2}}=\dfrac{5}{4\sqrt{2}} -\dfrac{3}{2\sqrt{2}}=\dfrac{5}{4\sqrt{2}} -\dfrac{6}{4\sqrt{2}}=-\dfrac{1}{4\sqrt{2}}\\\\\\=-\dfrac{1\times\sqrt{2} }{4\sqrt{2}\times\sqrt{2} }=-\dfrac{\sqrt{2} }{8 }=-\dfrac{1 }{8 }\sqrt{2}\ .[/tex]
