Question

aratati ca sunt patrate perfecte:
1000(puterea a 2) -1000-999

1+2+3....+1000+501*1001

Answer 1

1000^2-1000-999=
1000(1000-1)-999=
1000*999-999=
999(1000-1)=
999*999 => patrat perfect

1+2+3+....+1000+501*1001=
gauss pentru suma
1000*1001/2=
500*1001

reintroducem rezultatul sumei in ecuatie
500*1001+501*1001=
1001(500+501)=
1001*1001=> patrat perfect

Answer 2

1000^2-1000-999=1000000-1000-999=999000-999=998001
998001=999^2

1+2+3+........+1000+501x1001=
1000x(1000+1):2+501501=1000x1001:2+501501=1001000:2+501501=500500+  501501=1002001
1002001=10001^2