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Arata ca ([tex]( \sqrt{5+2\sqrt{6} } - \sqrt{5-2\sqrt{6}} -2\sqrt2 )^{2014} =0[/tex]

Răspuns :

Miaumiau
observa ca :   [tex](\sqrt{2}+\sqrt{3})^2=5+2\sqrt{6}.[/tex]

Atunci expresia ta este:

[tex][\sqrt{2}+\sqrt{3}-(\sqrt{3}-\sqrt{2})-2\sqrt{2}]^{2014}=\\ \\ =[2\sqrt{2}-2\sqrt{2}]^{2014}=\\ \\ =0^{2014}\\ \\ =0[/tex]

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