Question

Arătaţi că √15n+17= nu aparţine Q ,pentru orice n ∈ ℕ

Answer 1

$Numarul~15n~are~ultima~cifra~egala~cu~0~sau~5. \\ Dumarul~15n+17~are~ultima~cifra~egala~cu~2~sau~7. \\ Un~patrat~perfect~poate~avea~ultima~cifra~egala~cu~0;~1;~4;~5;~6;~9. \\ Asadar,~15n+17~nu~este~patrat~perfect,~si,~prin~urmare \\ \sqrt{15n+17} \notin Q.$