Question

Calculați: √5 supra 2-√5 + 2 supra 2+√5 .
Vă rog ,mult cine mă poate ajuta.

Answer 1

√5/(2-√5) +2/(2+√5)=√5(2+√5)/(4-5) +2(2-√5)/(4-5)=-1(2√5+5+4-2√5)=-1*9=-9

Answer 2

   
[tex]\displaystyle\\ \frac{ \sqrt{5} }{2-\sqrt{5} }+ \frac{2}{2+\sqrt{5} } =\\\\\\ = \frac{ \sqrt{5} (2+\sqrt{5})}{(2-\sqrt{5})(2+\sqrt{5}) }+ \frac{2(2-\sqrt{5})}{(2-\sqrt{5})(2+\sqrt{5})}=\\\\\\ = \frac{ 2\sqrt{5} +5}{4-5 }+ \frac{4-2\sqrt{5}}{4-5}=\frac{ 2\sqrt{5} +5+4-2\sqrt{5}}{-1}= \frac{5+4}{-1} =\boxed{-9} [/tex]