Question

Determinati numerele prime a si b , daca ab+ba=99

REPEDE Va roggggggggggg

Answer 1

$\displaystyle\bf\\\overline{ab}+\overline{ba}=10a+b+10b+a=11a+11b=11(a+b)=99,\\impartim~ambii~membri~la~11 \implies \boxed{\bf a+b=9}.\\avand~ca~numerele~a~si~b~sunt~cifre~prime,~iar~suma~lor\\este~un~numar~impar,~una~din~cifre~este~para,~cum~singurul~numar~prim\\par~este~2~una~din~cifre~este~2~urmand~ca~cealalta~sa~fie~7.\\deci,~\boxed{\bf (a,b)\in\left\{(2,7),(7,2)\left\}}.$