[tex]n=(2 \sqrt{3} - \sqrt{2} )^2-( \sqrt{6} -2)^2 \\ n=(2 \sqrt{3} )^2-2*2 \sqrt{3} * \sqrt{2} + \sqrt{2} ^2-( \sqrt{6} ^2-2* \sqrt{6} *2+2^2) \\ n=12-4 \sqrt{6} +2-(6-4 \sqrt{6} +4) \\ n=12-4 \sqrt{6} +2-6+4 \sqrt{6} -4 \\ n=12+2-6-4 [/tex]
[tex]n=4 [/tex] ∈ [tex]N[/tex]
[tex](5x+1)^2-2(5x+1)(5x-1)-(5x-1)^2= \\ =(5x)^2-2*5x*1+1^2-2(25x^2-1)-[(5x)^2-2*5x*1+1^2]= \\ =25x^2-10x+1-50x^2+2-(25x^2-10x+1)= \\ =25x^2-10x+1-50x^2+2-25x^2+10x-1=-50x^2+2[/tex]