Question

stabiliti daca numarul n=(2√3-√2)²-(√6-2)² este natural
Calculați (5x+1)²-2(5x+1)(5x-1)-(5x-1)²=

Answer 1

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