Question

2+√3 + 2-√3=

------- ------

1-√5 1+√5=

 

essa dois calculos são da mesma conta

Answer 1

Temos que:

 

$\dfrac{2+\sqrt{3}}{1-\sqrt{5}}+\dfrac{2-\sqrt{3}}{1-\sqrt{5}}$

 

Desta maneira:

 

$=\dfrac{(2+\sqrt{3})\cdot(1+\sqrt{5})+(2-\sqrt{3})\cdot(1-\sqrt{5})}{(1-\sqrt{5})\cdot(1+\sqrt{5})}$

 

$=\dfrac{2+\sqrt{3}+2\sqrt{5}+\sqrt{15}+2-2\sqrt{5}-\sqrt{3}+\sqrt{15}}{1^2-(\sqrt{5})^2}$

 

$=\dfrac{4}{-4}=-1$