Question

204+2(1+2+...+203)
1215+2•(1+2+..+1214)
125+2•(1+2+....+124)
Aratati ca nu sunt patrate perfecte.
Urgent!

Answer 1

204 + 2(1+2+...+203) =
= 204 + 2 × 203 × 204 : 2 =
= 204 + 203 × 204 =
= 204 × (1 + 203) =
= 204 × 204 =
= 204^2 este patrat perfect

1215 + 2×(1+2+...+1214) =
= 1215 + 2× 1214 × 1215 : 2 =
= 1215 + 1214 × 1215 =
= 1215 × ( 1 + 1214) =
= 1215 × 1215 =
= 1 215^2 este patrat perfect

125 + 2 × (1+2+...+124) =
= 125 + 2 × 124 × 125 : 2 =
= 125 + 124 × 125 =
= 125 × ( 1 + 124) =
= 125 × 125 =
= 125^2 este patrat perfect