Question

aratati ca x=3(1+3+5+......2017)-1009×2018 este patrat perfect​

Answer 1

Răspuns:

x = 1009² = patrat perfect

Explicație pas cu pas:

x = 3·(1+3+5+......2017)-1009×2018 <=>

x = 3·(1+2017)·[(2017-1):2+1]:2 - 1009×2018 =>

x = 3·2018·1009:2 - 1009·2018 =>

x = 3·1009·1009 - 1009·1009·2 =>

x = 1009·1009·(3-2) =>

x = 1009·1009 =>

x = 1009² = patrat perfect