Question

e) (x + 1)^3 - (x - 1)^3 - 6(x - 1)^2 = -19.

Answer 1

\(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x-1\right)^2=-19\\ \Leftrightarrow x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6=-19\\ \Leftrightarrow12x=-15\\ \Leftrightarrow x=-\dfrac{15}{12}=-\dfrac{5}{4}\)

Answer 2

\(\Leftrightarrow\)\(x^3+3x^2+3x+1-(x^3-3x^2+3x-1)-(6x^2-12x+6)+19=0\)

\(\Leftrightarrow\)\(x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6+19=0\)

\(\Leftrightarrow\)\(12x+15=0\)

\(\Leftrightarrow\)\(x=-\dfrac{5}{4}\)