Question

Sabendo que a sequencia (-1,×,4×+3) p.g ,encontre os valores de ×

Answer 1

$Ol\acute{a}~~ Regina \\ \\ Sendo~a~\boxed{P.G\{ a_{1},a_{2},a_{3},a_{a},.......\} } \\ \\ A ~ raz\tilde{a}o~\acute{e}: \\ \\ \boxed{q= \frac{a_{2}}{a_{1}} = \frac{a_{3}}{a_{2}} =..........} \\ \\ Ent\tilde{a}o~com~essa~condi\zeta\tilde{a}o~resolvemos: \\***************************************** \\ Sendo~a~sequencia: \\ (-1,x,4x+3)$

$Ent\tilde{a}o: \\ \\\boxed{ q= \frac{x}{-1}}----\ \textgreater \ (I)~~~e~~~~\boxed{q= \frac{4x+3}{x} }-----\ \textgreater \ (II) \\ \\~~~~~~~~~~~~~~~~ (I)=(II) \\ Igualando~tenemos: \\ \\ \frac{x}{-1}= \frac{4x+3}{x} ~~~---\ \textgreater \ desenvolviendo~temos: \\ \\ -x.x=4x+3 \\ \\ - x^{2} =4x+3 \\ \\ - x^{2} -4x-3=0~~~--\ \textgreater \ multiplicamos~por~(1)~fica: \\ \\ x^{2} +4x+3=0$

$Bucaremos~dois~n\acute{u}meros~multiplicados~resulte(+3)~e ~somado (+4) \\ \\ dois~n\acute{u}mero~multiplicados--\ \textgreater \ +1.(+3)=+3 \\ dois~n\acute{u}mero~ somados----\ \textgreater \ +1+3=+4 \\ \\ Ent\tilde{a}o~os~n\acute{u}meros ~s\tilde{a}o~~ temos: \\ \\ (x+1)(x+3)=0$

$Igualando~os~produtos~a~zero~temos: \\ \\ (x+1)=0~~~~~e~~~~~(x+3)=0 \\ \\ ~~~~~~~~x'=-1~~~~~~~~~~~~~~~x''=-3 \\ \\ C.S\{-1,-3\}$

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                                   espero ter ajudado!!