Question

Aratati ca numarul a este patrat perfect:
a) a=(1+2+3+...+99)x2+100
b) a=1+2+3+...+50-25x50
c) a=3+6+9+...+75-75
e urgent!! va rog!!

Answer 1

a) a=(1+2+3+...+99)x2+100=99×100:2×2+100=
=99×100+100=100(99+1)=100×100=100² deci patrat perfect

b) a=1+2+3+...+50-25x50 =50×51:2-25×50=25×51-25×50=25(51-50)=25=5² deci patrat perfect

c) a=3+6+9+...+75-75=3(1+2+3+....+25)-75=3×25×26:2-75=75×13-75=
=75(13-1)=75×12=3×5²×3×2²=(2×3×5)²=30² deci patrat perfect