URGENTT SLP!!!!!!!!!!!!!!!!

Bonjour  Crazyox 

[tex]\sqrt{4+\sqrt{12}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}\\\\=\sqrt{4+\sqrt{4\times3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\sqrt{2+2\sqrt{6}+3}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\sqrt{\dfrac{4+4\sqrt{6}+6}{2}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\sqrt{\dfrac{(2+\sqrt{6})^2}{2}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{\sqrt{(2+\sqrt{6})^2}}{\sqrt{2}}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{2+\sqrt{6}}{\sqrt{2}}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{(2+\sqrt{6})\times\sqrt{2}}{\sqrt{2}\times\sqrt{2}}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{2\sqrt{2}+\sqrt{6}\sqrt{2}}{2}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{2\sqrt{2}+\sqrt{12}}{2}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{2\sqrt{2}+2\sqrt{3}}{2}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\dfrac{2(\sqrt{2}+\sqrt{3})}{2}}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-(\sqrt{2}+\sqrt{3})+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\sqrt{2}-\sqrt{3}+\sqrt{2}[/tex]

[tex]\\\\=\sqrt{4+2\sqrt{3}}-\sqrt{3}[/tex]

[tex]\\\\=\sqrt{1+2\sqrt{3}+3}-\sqrt{3}[/tex]

[tex]\\\\=\sqrt{1+2\sqrt{3}+(\sqrt{3})^2}-\sqrt{3}[/tex]

[tex]\\\\=\sqrt{(1+\sqrt{3})^2}-\sqrt{3}[/tex]

[tex]\\\\=(1+\sqrt{3})-\sqrt{3}[/tex]

[tex]=1[/tex]

Par conséquent,

[tex]\boxed{\sqrt{4+\sqrt{12}}-\sqrt{5+2\sqrt{6}}+\sqrt{2}=1}[/tex]

soit 

[tex]\boxed{a-b+\sqrt{2}=1}[/tex]