Respostas

  • Usuário do Brainly
2013-06-27T17:11:36-03:00

a) 2\cdot(\text{x}^2-1)=\tex{x}^2+7

 

2\text{x}^2-2=\text{x}^2+7

 

\text{x}^2=9

 

Logo:

 

\text{x}=\pm\sqrt{9}=\pm3

 

\text{S}=\{-3, 3\}

 

 

b) 5\cdot(\text{x}^2-1)=4\cdot(\text{x}^2+1)

 

5\text{x}^2-5=4\text{x}+4

 

\tex{x}^2=9

 

Logo:

 

\tex{x}=\pm\sqrt{9}=\pm3

 

\text{S}=\{-3, 3\}

 

 

c) (\text{x}-5)\cdot(\text{x}+4)+8=\text{x}

 

\text{x}^2+4\text{x}-5\text{x}-20+8=\text{x}

 

\text{x}^2-2\text{x}-12=0

 

Desta maneira:

 

\text{x}=\dfrac{-(-2)\pm\sqrt{(-2)^2-4\cdot1\cdot(-12)}}{2\cdot1}=\dfrac{2\pm2\sqrt{13}}{2}

 

Logo:

 

\text{x}'=\dfrac{2+2\sqrt{13}}{2}=1+\sqrt{13}

 

\text{x}"=\dfrac{2-2\sqrt{13}}{2}=1-\sqrt{13}

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