Question

p=(√5 + √2)² - √2(√5 + √2) -√5(√2 - 2√5)
Aratati ca p este nr. naturatl.

Answer 1

P=(√5 + √2)² - √2(√5 + √2) -√5(√2 - 2√5)
 P=5+2√10+2-√10-2-√10+10
P=15

Answer 2

               
$P = \\ =( \sqrt{5} + \sqrt{2} )^2 - \sqrt{2}( \sqrt{5} + \sqrt{2} ) - \sqrt{5}( \sqrt{2} - 2\sqrt{5})= \\ =( \sqrt{5} + \sqrt{2} )(\sqrt{5} + \sqrt{2}-\sqrt{2})+\sqrt{5}(2\sqrt{5} - \sqrt{2})= \\ =( \sqrt{5} + \sqrt{2} )(\sqrt{5}) +\sqrt{5}(\sqrt{5} +\sqrt{5} - \sqrt{2})= \\ =\sqrt{5}( \sqrt{5} + \sqrt{2} ) +\sqrt{5}(\sqrt{5}) +\sqrt{5}(\sqrt{5} - \sqrt{2})= \\ =\sqrt{5}( \sqrt{5} + \sqrt{2} ) +5 +\sqrt{5}(\sqrt{5} - \sqrt{2})= \\ =\sqrt{5}( \sqrt{5} + \sqrt{2} ) +\sqrt{5}(\sqrt{5} - \sqrt{2}) + 5=$

$=\sqrt{5}( \sqrt{5} + \sqrt{2} +\sqrt{5} - \sqrt{2}) + 5= \\ =\sqrt{5}( \sqrt{5} +\sqrt{5}+ \sqrt{2} - \sqrt{2}) + 5= \\ =\sqrt{5}( 2\sqrt{5} ) + 5= \\ =2\sqrt{5}*\sqrt{5}+5 = 2*5+5=10+5= \boxed{15}$