Question

Rezolvați in R ecuația :
x-1\7 + x-2\7+x-3\7+...+x-99\7 .

Answer 1

$\frac{x-1}{7} + \frac{x-2}{7}+ \frac{x-3}{7}+...+ \frac{x-99}{7}=0 <=>\\<=> \frac{(x-1)+(x-2)+(x-3)+...+(x-99)}{7} =0 => \\ =>(x-1)+(x-2)+(x-3)+...+(x-99)=0<=> \\ <=>99x-(1+2+3+...+99)=0<=> \\ <=>99x- \frac{99*100}{2} =0<=> \\ <=>99x-99*50 <=> \\ <=> 99x=99*50=>x=50 \\ \\ Solutie:~x=50.$