exerc.resolvido

por **adauto martins** » Sex Out 18, 2019 23:26

(UFRRJ-universidade federal rural do rj-exame vestibular 1961)
resolva a equaçao

$2\sqrt[n]{(1-x)}+\sqrt[n]{(1+x)}=3\sqrt[2n]{(1-{x}^{2})}$

por **adauto martins** » Sáb Out 19, 2019 00:48

soluçao:

$2\sqrt[n]{(1-x)}+\sqrt[n]{(1+x)}=3\sqrt[2n]{(1-{x}^{2})}=3.\sqrt[2n]{(1-x).(1+x)}$

$(2.\sqrt[n]{(1-x)}+\sqrt[n]{(1+x)})/(\sqrt[2n]{(1-x).(1+x)}=3 (2.\sqrt[n]{(1-x)})/(\sqrt[2n]{(1-x).(1+x)})+(\sqrt[n]{(1+x)})/(\sqrt[2n]{(1-x).(1+x)})=3$

sabendo que:
$\sqrt[n]{(1-x)}/\sqrt[2n]{(1-x)(1+x)}=(1-x)^{((1/n))}/((1-x)^{(1/2n)}.(1+x)^{(1/2n)})=(1-x)^{((1/n)-(1/2n))}/(1+x)^{(1/2n)}=(1-x)^{(1/2n)}/(1+x)^{(1/2n)} =\sqrt[2n]{(1-x)/(1+x)}$

fazendo $y=\sqrt[2n]{(1-x)/(1+x)}$

teremos:
$2.y+(1/y)=3\Rightarrow 2{y}^{2}-3y+1=0...$

achar os valores de y,e consequentemente os valores de x...termine-o

exerc.resolvido

exerc.resolvido

exerc.resolvido

Re: exerc.resolvido

Quem está online