Question

Aratati ca numarul x=1010+2+4+6+8+...+2018 este patrat perfect si calculati √x(radical din x)​

Answer 1

1010+2+4+6+....+2018

1010+2*1+2*2+2*3+.....+1009*2

1010*2*(1+2+3+....+1009)

1010*2*1009*(1009+1):2

1010*1009*1010

1010*1009+1)

1010²

√x=√1010²=1010

Answer 2

Răspuns:

x=1010+2(1+2+3+4+..+1009)

x=1010+2·(1009·1010):2

x=1010+1009·1010

x=1010(1+1009)

x=1010·1010

x=1010² este patrat perfect

√x=√1010²=1010