Question

Fie numerele a=$\sqrt{9-2 \sqrt{14} }$ si b=$\sqrt{9+2 \sqrt{14} }$ . Aratati ca ( a-b +2√2)la puterea 2013 ∈ N . Va rog mult sa ma ajutati sa calculez numerele ca la partea a doua ma descurc!

Answer 1

√(9-2√14)=√(9-√56)=√(9+√81-56)/2-√(9-√81-56)/2=√(9+√25)/2-√(9-√25)/2=
=√(9+5)/2-√(9-5)/2=√7-√2
√(9+2√14)=√(9+√56)=√(9+√81-56)/2+√(9-√81-56)/2=√(9+√25)/2+√(9-√25)/2=
=√(9+5)/2+√(9-5)/2=√7+√2
a-b+2√2=[√7-√2-(√7+√2)+2√2]²⁰¹³=[√7-√2-√7-√2+2√2]²⁰¹³=0²⁰¹³=0