Question

determine o alor das equaçoes do 2 grau : X ao quadrado - 2x sobre 4 =1sobre 4 + x sobre 2

Answer 1

Temos que:

 

$\dfrac{\text{x}^2-2\text{x}}{4}=\dfrac{1}{4}+\dfrac{\text{x}}{2}$

 

$\text{x}^2-2\text{x}=1+2\text{x}$

 

$\text{x}^2-4\text{x}-1=0$

 

Desta maneira:

 

$\text{x}=\dfrac{-(-4)\pm\sqrt{(-4)^2-4\cdot1\cdot(-1)}}{2\cdot1}=\dfrac{4\pm2\sqrt{5}}{2}$

 

Logo:

 

$\text{x}'=\dfrac{4+2\sqrt{5}}{2}=2+\sqrt{5}$

 

$\text{x}"=\dfrac{4-2\sqrt{5}}{2}=2-\sqrt{5}$