Question

1.Stind ca a·b=79 si b·c=49,calculati :b·(a-c)
2.Demonstrati ca nr 1·2·3·...·1999+2 nu e patrat perfect.

Answer 1

$\boxed{1.}~ b(a-c)=ab-bc=79-49=30. \\ \\ \boxed{2.}~1 \cdot 2 \cdot 3 \cdot... \cdot 1999~are~ultima~cifra~cifra~egala~cu~0,~deoarece \\ \\ in~contine~pe~10~ca~factor. \\ \\ \Rightarrow 1 \cdot 2 \cdot 3 \cdot... \cdot 1999 +2~are~ultima~cifra~egala~cu~2,~insa \\ \\ niciun~patrat~perfect~nu~are~ultima~cifra~egala~cu~2 \Rightarrow~numarul~nu~ \\ \\ este~patrat~perfect.$