Question

Exercitiul 4

Va rog repede

Answer 1

Răspuns:

a) $b=\sqrt{1+3+5+...2019}=\sqrt{2020(2018:2+1):2} =\sqrt{1010*1010} =1010$∈N

b) $a=\sqrt{2015n+2018}$

daca n=2k ⇒ n+1=2k+1

      u(2015(2k+1)+2018)=u(5+8)=3 ⇒2015n+2018≠p²   (1)

daca n=2k+1 ⇒ n+1=2k+2

      u(2015(2k+2)+2018)=u(0+8)=8 ⇒2015n+2018≠p²   (2)

(1), (2) ⇒ a≠p²

Explicație pas cu pas:

Patratele perfecte pot avea ca ultima cifra doar pe 0, 1, 4, 5, 6, 9.