Question

Determine os números q possuem modulo igual a 1

Answer 1

$\Large\boxed{\begin{array}{l}\underline{\rm D~\!\!efinic_{\!\!,}\tilde ao~de~m\acute odulo}\\\sf |x|=\begin{cases}\sf x,se~x\geqslant0\\\sf-x,se~x<0\end{cases}\\\sf \underline{\rm Propriedade~do~m\acute odulo}\\\sf seja~a~um~n\acute umero~real~tal~que~a>0.\\\sf ent\tilde ao\\\sf |x|=a\iff x=a~ou~x=-a.\\\rm Determine~os~n\acute umeros\\\rm que~possuem~m\acute odulo~igual~1.\\\underline{\boldsymbol{Soluc_{\!\!,}\tilde ao}}\\\sf sendo~a=1~e~x~o~n\acute umero\\\sf~procurado~podemos~escrever:\\\sf \end{array}}$

$\Large\boxed{\begin{array}{l}\sf|x|=1\\\sf como~1>0~podemos~aplicar~a~propriedade\\\sf x=1~ou~x=-1.\\\sf S=\{-1,1\}\\\sf ou~seja~os~n\acute umeros~que~possuem\\\sf~m\acute odulo~igual~1~s\tilde ao~-1~e~1.\end{array}}$