Question

Aratati ca $\frac{2}{ \sqrt{3} -1} - \sqrt{3} =1$

Answer 1

Ducem pe 1 de cealalta parte a egalitatii
$\frac{2}{\sqrt{3}-1}-\sqrt{3}-1=0\Rightarrow \frac{2}{\sqrt{3}-1}-(\sqrt{3}+1)=\frac{2-(\sqrt{3}-1)(\sqrt{3}+1)}{2}=0\Rightarrow 2-(3-1)=2-2=0$
Ceea ce este adevarat

Answer 2

2/(√3-1) se rationalizeaza si devine 2(√3+1)/2=√3+1
=>√3+1-√3=1 - adevarat