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Exercitiul 1 de la partea a II a!!!

Exercitiul 1 De La Partea A II A class=

Răspuns :

a=√(3-√5)-√(3+√5)
formula radicali compusi
√(3-√5)=√[3+√(9-5)]/2-√[3-√(9-5)]/2=√(3+2)/2-√(3-2)/2=√5/2-√1/2
√(3+√5)=√[3+√(9-5)]/2+√[3-√(9-5)]/2=√(3+2)/2+√(3-2)/2=√5/2+√1/2
a=√(3-√5)-√(3+√5)=√5/2-√1/2-(√5/2+√1/2)=√5/2-√1/2-√5/2-√1/2=-2√1/2
a²=(-2√1/2)²=4/2=2
a²∈N