Question

Ajutorr!!!  Aflati numerele naturale x:
a) 5+2 (x+1)=5 (x-1);
b) 3^x+3^x+1+3^x+2=117;
c) x+2x+3x+....+100x=1000.

Answer 1

a) 5+2 (x+1)=5 (x-1);
5+2x+2=5x-5
7+2x=5x-5
7+5=5x-2x
12=3x
12:3=x
x=4


b) 3^x+3^x+1+3^x+2=117;

3^x(1+3+3²)=117

3^x*13=117

3^x=117:13

3^x=9

3^x=3²

x=2
c) x+2x+3x+....+100x=1000.
x(1+2+3+...+100)=1000
x*100*101:2=1000
x*5050=1000
x=1000:5050

sigur aici e asa?