Question

Aratati ca radical din 2011 la X+1 este irational (clsa a7 a problema 14 punctul a pagina 125 sem 1)

Answer 1

Caz a) x impar x=2p+1
√(2011)^(2p+1+1)=√(2011)^(2p+2)= √[(2011)^(p+1)]²=2011^ (p+1) RATIONAL

Caz b) x par, x=2p
√(2011)^(2p+1)= √(2011)^2p *201=√(2011)^2p * √2011=
   √(2011^p^2) * √2011=(2011^p)* √2011 IRATIONAL