Question

(x+1)^3-(x-1)^3-6(x-1)^2= -10

Answer 1

\(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-10\)\(\Leftrightarrow x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-2x+1\right)=-10\)\(\Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6=-10\)

\(\Leftrightarrow x^3-x^3+3x^2+3x^2-6x^2+3x-3x+12x-4=-10\)

\(\Leftrightarrow12x=-10+4\)

\(\Leftrightarrow12x=-6\)

\(\Leftrightarrow x=-\dfrac{1}{2}\)

\(S=\left\{\dfrac{-1}{2}\right\}\)