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Boa noite Alexandre!
Solução!
![\sqrt{x+6}=x\\\\\\
( \sqrt{x+6} )^{2}=(x)^{2}\\\\\\
x+6= x^{2} \\\\\
x^{2} -x-6=0](https://tex.z-dn.net/?f=+%5Csqrt%7Bx%2B6%7D%3Dx%5C%5C%5C%5C%5C%5C%0A%28+%5Csqrt%7Bx%2B6%7D+%29%5E%7B2%7D%3D%28x%29%5E%7B2%7D%5C%5C%5C%5C%5C%5C%0Ax%2B6%3D+x%5E%7B2%7D+%5C%5C%5C%5C%5C%0A+x%5E%7B2%7D+-x-6%3D0 "\sqrt{x+6}=x\\\\\\
( \sqrt{x+6} )^{2}=(x)^{2}\\\\\\
x+6= x^{2} \\\\\
x^{2} -x-6=0")
![x= \dfrac{1\pm \sqrt{(-1) ^{2}-4.1.-6 } }{2.1} \\\\\\
x= \dfrac{1\pm \sqrt{1+24 } }{2} \\\\\\
x= \dfrac{1\pm \sqrt{25 } }{2} \\\\\\
x= \dfrac{1\pm5}{2} \\\\\\\\\\
Raizes\\\\\\\
x_{1}= \frac{1+5}{2}= \dfrac{6}{2}=3 \\\\\\\
x_{2}= \frac{1-5}{2}= \dfrac{-4}{2}=-2~~nao~~serve\\\\\\\\\\\
\boxed{Resposta: x_{1}=3~~Alternativa~~B}](https://tex.z-dn.net/?f=%0A%0Ax%3D++%5Cdfrac%7B1%5Cpm+%5Csqrt%7B%28-1%29+%5E%7B2%7D-4.1.-6+%7D+%7D%7B2.1%7D+%5C%5C%5C%5C%5C%5C%0Ax%3D++%5Cdfrac%7B1%5Cpm+%5Csqrt%7B1%2B24+%7D+%7D%7B2%7D+%5C%5C%5C%5C%5C%5C%0Ax%3D++%5Cdfrac%7B1%5Cpm+%5Csqrt%7B25+%7D+%7D%7B2%7D+%5C%5C%5C%5C%5C%5C%0A%0Ax%3D++%5Cdfrac%7B1%5Cpm5%7D%7B2%7D+%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0ARaizes%5C%5C%5C%5C%5C%5C%5C%0A+x_%7B1%7D%3D+%5Cfrac%7B1%2B5%7D%7B2%7D%3D+%5Cdfrac%7B6%7D%7B2%7D%3D3++%5C%5C%5C%5C%5C%5C%5C%0A+x_%7B2%7D%3D+%5Cfrac%7B1-5%7D%7B2%7D%3D+%5Cdfrac%7B-4%7D%7B2%7D%3D-2%7E%7Enao%7E%7Eserve%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%5C%0A%5Cboxed%7BResposta%3A+x_%7B1%7D%3D3%7E%7EAlternativa%7E%7EB%7D+%0A%0A "x= \dfrac{1\pm \sqrt{(-1) ^{2}-4.1.-6 } }{2.1} \\\\\\
x= \dfrac{1\pm \sqrt{1+24 } }{2} \\\\\\
x= \dfrac{1\pm \sqrt{25 } }{2} \\\\\\
x= \dfrac{1\pm5}{2} \\\\\\\\\\
Raizes\\\\\\\
x_{1}= \frac{1+5}{2}= \dfrac{6}{2}=3 \\\\\\\
x_{2}= \frac{1-5}{2}= \dfrac{-4}{2}=-2~~nao~~serve\\\\\\\\\\\
\boxed{Resposta: x_{1}=3~~Alternativa~~B}")
Boa noite!
Bons estudos!
Solução!
Boa noite!
Bons estudos!
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