Question

Solutia numar natural a ecuatiei 10x+11x+12x+....+99x=9810 este
a) 2
b) 0
c) 1
d) 3

Answer 1

folosim formula 1+2+3+4+...+n=$\frac{n*(n+1)}{2}$

1+2+3+4+...+99=$\frac{99*100}{2}= 4950$
1+2+3+4+...+9=$\frac{9*10}{2}=45$

10+11+12+...+99=4950-45=4905

10x+11x+12x+...+99x=9810
x(10+11+12+...+99)=9810
4905x=9810
x=9810:4905
x=2