Question

Impartind numarul x la numarul y, se obtine catul 3 si restul 7.
a) Calculati 2x-6x+3.
b) Aratati ca x+y>35.

Answer 1

[tex]\it{x:y=3\ rest 7 }[/tex]

Aplicam teorema impartirii cu rest si obtinem relatiile :

$\it{x=3y+7\ \ \ \ (1)}$

$\it{y\ \textgreater \ 7\ \ \ \ (2)}$

Acum avem:

$\it{y\ \textgreater \ 7|_{\cdot3}\Longrightarrow 3y\ \textgreater \ 21|_{+7}\Longrightarrow 3y+7\ \textgreater \ 28\stackrel{(1)}{\Longrightarrow} x\ \textgreater \ 28}$

Deci:

$x\ \textgreater \ 28\ si\ y\ \textgreater \ 7\Longrightarrow \ x+y\ \textgreater \ 28+7 \Longrightarrow \ x+y\ \textgreater \ 35 .$