Question

x+2/1+ x+3/2 + x+4/3 + ... + x+19/18 + x+20/19=19

(si x face parte din fractii)​

Answer 1

Răspuns:

Explicație pas cu pas:

$\frac{x+2}{1}+ \frac{x+3}{2}+ \frac{x+4}{3}+...+\frac{x+19}{18}+\frac{x+20}{19}=\frac{x}{1}+\frac{2}{1}+\frac{x}{2}+\frac{3}{2}+\frac{x}{3}+\frac{4}{3}+...+\frac{x}{18}+\frac{19}{18}+\frac{x}{19}+\frac{20}{19}=x*(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19})+1+1+1+\frac{1}{2}+1+\frac{1}{3}+...+1+\frac{1}{18}+1+\frac{1}{19}=x*(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19})+(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19})+19\\Deci~x*(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19})+(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19}) +19=19\\x*(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19})+(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19}) =0\\(\frac{1}{1}+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{18}+\frac{1}{19})*(x+1)=0,~deci~x+1=0,~x=-1.$