Question

Efectuati calculele

Answer 1

[tex](\sqrt7-\sqrt6)(\sqrt{7}+\sqrt6)^{2011}-(\sqrt7-2)^2+(\sqrt7+3)^2 = \\ \\ =(\sqrt7-\sqrt6)\cdot (\sqrt7+\sqrt6)^{1+2010} - (\sqrt7^2-2\cdor \sqrt7\cdot 2+2^2)+\\ +(\sqrt7^2+2\cdot \sqrt7\cdot 3+3^2) = \\ \\ = (\sqrt7-\sqrt6)\cdot (\sqrt7+\sqrt6)\cdot (\sqrt7+\sqrt6)^{2010} -(7-4\sqrt7+4)+ \\ +(7+6\sqrt7+9) = \\ \\ = \Big(\sqrt7^2-\sqrt6^2\Big)\cdot (\sqrt7+\sqrt6)^{2010}-(11-4\sqrt7)+16+6\sqrt7 = \\ \\ = (7-6)\cdot (\sqrt7+\sqrt6)^{2010}-11+4\sqrt7+16+6\sqrt7 =[/tex]

$= 1\cdot (\sqrt7+\sqrt6)^{2010}+5+10\sqrt7= \\ \\ = (\sqrt7+\sqrt6)^{2010}+5+10\sqrt7$