Question

Aflați nr.naturale x:
3lax+3lax+1+3lax+2=117;
x+2x+3x+....+100x=10100.

Answer 1

3 la x+3lax+1+3lax+2=117
3la x factor comun

3lax(1+3la1+3la2)=117
3la x inmultit cu 13=117
3lax=117:13
3lax =9
3la x=3la 3
=>x=3

x+2x+3x+...+100x=10100
dam pe x factor comun

x(1+2=3+...100)=10100
aplicam formula sumei lui Gauss
x(100x101):2=10100
x inmultit cu 10100=10100inmultit cu 2
10100X=20200
x=2