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calculati [tex] \sqrt{7+ \sqrt{7} } [/tex] · [tex]\sqrt{ \sqrt{14}+ \sqrt{7+ \sqrt{7} } }[/tex] · [tex]\sqrt{ \sqrt{14}- \sqrt{7+ \sqrt{7} } }[/tex]

Răspuns :

[tex] \sqrt{7+ \sqrt{7} }* \sqrt{ \sqrt{14} + \sqrt{7+ \sqrt{7} } } *\sqrt{ \sqrt{14} - \sqrt{7+ \sqrt{7} } } =[/tex]

[tex]= \sqrt{7+ \sqrt{7} } *\sqrt{ \sqrt{14}^2 - \sqrt{7+ \sqrt{7} }^2 } =[/tex]

[tex]= \sqrt{7+ \sqrt{7} } *\sqrt{ 14 -7+ \sqrt{7} } = [/tex]

[tex]= \sqrt{7+ \sqrt{7} } *\sqrt{ 7+ \sqrt{7} } = [/tex]

[tex]= \sqrt{7+ \sqrt{7} }^2=[/tex]

[tex]=7+ \sqrt{7} [/tex]