Question

numerele prime x,y,z, daca: 2*x+6*y+z=38
*= ori
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Answer 1

$\displaystyle\bf\\2x+6y+z=38,~stim~ca~2x,~6y~sunt~mereu~pare,~pentru~orice\\x,y \in \mathbb{N}. \\suma~a~trei~numere,~dintre~care~2~numere~sunt~pare,~este~un~numar~\\par,~daca~si~cel~de~al~treilea~este~par \implies z=prim~si~par~\implies~\boxed{\bf z=2}~.\\2x+6y+2=38 | :2 \Leftrightarrow x+3y+1=19 \Leftrightarrow 3y+x=18\Leftrightarrow 3y=18-x.\\18-x=\mathcal{M}_3 \Leftrightarrow \mathcal{M}_3 - x = \mathcal{M}_3 \implies x=\mathcal{M}_3,~dar~x~este~prim,~deci~\boxed{\bf x=3}~.$

$\displaystyle\bf\\facem~o~simpla~inlocuire.\\18-3=15=3y \implies \boxed{\bf y=5}.$