Question

Sa se arate ca √(6+4√2)∈{a+b√2 | a;b ∈ Z}
As dori raspuns complet , Multumesc!

Answer 1

$\sqrt{6+4 \sqrt{2}}= \sqrt{4+4 \sqrt{2} +2}= \sqrt{(2+ \sqrt{2})^2}=|2+ \sqrt{2}|=2 + \sqrt{2}. \\ \\ In~acest~caz~avem~a=2~si~b=1~( \in Z) \Rightarrow \\ \\ \Rightarrow \sqrt{6+4 \sqrt{2}} \in \{a+b \sqrt{2}~|~a,b \in Z \}.$