Respostas
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Boa tarde Amanda!
Solução!
Vamos elevar todos os membros da equação ao quadrado para cancelar com o índice da raiz,para determinarmos o conjunto verdade.
![3 \sqrt{3x+1}= \sqrt{18}\\\\\\
(3 \sqrt{3x+1})^{2}=( \sqrt{18})^{2}\\\\\\\
9(3x+1)=18\\\\\\
27x+9=18\\\\\\
27x=18-9\\\\\\
27x=9\\\\\\
x= \dfrac{9}{27}\\\\\\\\
Simplificando~~por~~9!\\\\\\
x= \dfrac{9:9}{27:9}\\\\\\\\
x= \dfrac{1}{3}\\\\\\\\
\boxed {Resposta:S=\{ \frac{1}{3}\}}](https://tex.z-dn.net/?f=3+%5Csqrt%7B3x%2B1%7D%3D+%5Csqrt%7B18%7D%5C%5C%5C%5C%5C%5C%0A%283+%5Csqrt%7B3x%2B1%7D%29%5E%7B2%7D%3D%28+%5Csqrt%7B18%7D%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%5C%0A9%283x%2B1%29%3D18%5C%5C%5C%5C%5C%5C%0A27x%2B9%3D18%5C%5C%5C%5C%5C%5C%0A27x%3D18-9%5C%5C%5C%5C%5C%5C%0A27x%3D9%5C%5C%5C%5C%5C%5C%0A%0Ax%3D+%5Cdfrac%7B9%7D%7B27%7D%5C%5C%5C%5C%5C%5C%5C%5C%0ASimplificando%7E%7Epor%7E%7E9%21%5C%5C%5C%5C%5C%5C%0A+x%3D+%5Cdfrac%7B9%3A9%7D%7B27%3A9%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A+x%3D+%5Cdfrac%7B1%7D%7B3%7D%5C%5C%5C%5C%5C%5C%5C%5C%0A%0A%5Cboxed+%7BResposta%3AS%3D%5C%7B+%5Cfrac%7B1%7D%7B3%7D%5C%7D%7D++++++ "3 \sqrt{3x+1}= \sqrt{18}\\\\\\
(3 \sqrt{3x+1})^{2}=( \sqrt{18})^{2}\\\\\\\
9(3x+1)=18\\\\\\
27x+9=18\\\\\\
27x=18-9\\\\\\
27x=9\\\\\\
x= \dfrac{9}{27}\\\\\\\\
Simplificando~~por~~9!\\\\\\
x= \dfrac{9:9}{27:9}\\\\\\\\
x= \dfrac{1}{3}\\\\\\\\
\boxed {Resposta:S=\{ \frac{1}{3}\}}")
Boa tarde!
Bons estudos!
Solução!
Vamos elevar todos os membros da equação ao quadrado para cancelar com o índice da raiz,para determinarmos o conjunto verdade.
Boa tarde!
Bons estudos!
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