Question

Решите уравнение. нужно. (x+1)^3-(x-1)^3=x(6x+2)

Answer 1

$(x+1)^3-(x-1)^3=x(6x+2)$

$(x+1-(x-1))((x+1)^2+(x-1)^2+(x+1)(x-1))=x(6x+2)$

$(x+1-x+1)(x^2+2x+1+x^2-2x+1+x^2-1)=6x^2+2x$

$2(3x^2+1)=6x^2+2x$

$6x^2+2=6x^2+2x$

$6x^2+2-6x^2-2x=0$

$2-2x=0$

$2x=2$

$x=1$

ответ: $1$

P. S.

$a^3-b^3=(a-b)(a^2+ab+b^2)$