Question

(√6-√2+√5) totul la puterea2

Answer 1

   
[tex]( \sqrt{6}- \sqrt{2} + \sqrt{5})^2 = \\ = \sqrt{6}\times \sqrt{6} -\sqrt{2}\times \sqrt{6}+\sqrt{5}\times \sqrt{6} - \\ -\sqrt{6}\times \sqrt{2} +\sqrt{2}\times \sqrt{2}-\sqrt{5}\times \sqrt{2} + \\ +\sqrt{6}\times \sqrt{5} -\sqrt{2}\times \sqrt{5}+\sqrt{5}\times \sqrt{5} = \\ =6-\sqrt{12}+\sqrt{30}-\sqrt{12}+2 - \sqrt{10}+\sqrt{30}-\sqrt{10}+5 = \\ =6+2+5 -2\sqrt{12}+2\sqrt{30} -2 \sqrt{10}= \boxed{13 +2(\sqrt{30}-\sqrt{12}-\sqrt{10})}[/tex]