wespe - revell/matchbox

[george93]

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[Claudiu Mindrila]

George93, daca ai nevoie de ajutor pentru tema la mate, poti folosi alte tipuri de forum-uri, nu cele destinate matematicii pentru concurs. Nu ma intelege gresit, dar in acest forum("Discutii pe clase (Olimpiada))" ne asteptam la probleme putin mai serioase. Posteaza problemele de genul acesteia la "Matematica la clasa", adica aici .

Sa rezolvam acum problema ta.
Problema.
Aflati \( x \) din ecuatia: \( \frac{x-2003}{5}+\frac{x-1999}{9}+\frac{x-1995}{13}+...+\frac{x-1951}{57}=14. \)
Solutie.
Sa remarcam ca este vorba de \( 14 \) termeni in suma ta, asa ca putem rescrie ecuatia astfel:
\( \frac{x-2003}{5}-1+\frac{x-1999}{9}-1+...+\frac{x-1951}{57}-1=0 \)
adica
\( (x-2008)\left(\frac{1}{5}+\frac{1}{9}+...\frac{1}{57} \right)=0 \).
Insa \( \frac{1}{5}+\frac{1}{9}+...\frac{1}{57}>0 \) de unde deducem ca \( x-2008=0\Longleftrightarrow x=2008. \)