Question

Aflati dacă x=pătrat perfect

x=3+6+9+12+...+864+41616





x= 3(1+3+5+7+...+2017)-1009x2018​

Answer 1

x=3+6+9+12+...+864+41616

x=3(1+2+3+…..+288)+41616

x=3•288•289:2 +41616

x=3·144•289+41616

x=3·41616+41616

x=4•41616

x=2²•204²=408²,  e patrat perfect

x= 3(1+3+5+7+...+2017)-1009•2018

x=3•[(2017+1):2]² -1009•2018

x=3•1009^2 -1009•2018

x=1009•(3•1009-2018)

x=1009•1009

x=1009² ,   e  patrat perfect