Question

fie a =2 la puterea2012+2 la puterea2013 si b=4 la puterea 1006+4 la puterea 1007.Calculati valoarea raportului a pe b

Answer 1

$a=2 ^{2012} +2 ^{2013}$
$a=2 ^{2012} *(1+2)=\ \textgreater \ a=3*2 ^{2012}$
$b=(2 ^{2} ) ^{1006} +(2 ^{2} ) ^{1007}$
$b=2 ^{2012} +2 ^{2014}$
$b=2 ^{2012} *(1+2 ^{2} )=\ \textgreater \ b=5*2 ^{2012}$
$=\ \textgreater \ \frac{a}{b} = \frac{3*2 ^{2012} }{5*2 ^{2012} } =\ \textgreater \ \frac{a}{b} = \frac{3}{5}$