Question

la suma de un numero y su reciproco es 26/5 halla los numeros (ecuaciones cuadraticas)

Answer 1

$Hola \\ \\ Sea~el~n\acute{u}mero~~---\ \textgreater \ \boxed{n} \\ \\ Y ~su~rec\acute{i}proco ~~---\ \textgreater \ \boxed{\frac{1}{n} } \\ Nos~dice: \\ \\ \underbrace{ La~suma~de~um~n\acute{u}mero~y~su~rec\acute{i}proco}_{\boxed{n+ \frac{1}{n}} }~\underbrace{es}_{=}~ 26/5 \\ \\ n+ \frac{1}{n}= \frac{26}{5}$


$5n\²+5=26n \\ \\ 5n\²-26n+5=0 \\ \\ (5n-1)(n-5)=0 \\ \\ 5n-1=0~~~~y~~~~n-5=0 \\ \\ 5n=1 ~~~~~~~~~~~~~~~~~~~~~\boxed{n''=5} \\ \\ \boxed{n'= \frac{1}{5} } \\ \\ C.S=\{ \frac{1}{5}~;~5 \}$

===================================================
                                  Espero haber ayudado!!