Question

Tìm x:

a) x(x+2)^2 - (x+1)^2=2

b) (x+2)^3-(x-3)^3

Answer 1

a: Ta có: \(x\left(x+2\right)^2-\left(x+1\right)^2=2\)

\(\Leftrightarrow x\left(x^2+4x+4\right)-x^2-2x-1-2=0\)

\(\Leftrightarrow x^3+4x^2+4x-x^2-2x-3=0\)

\(\Leftrightarrow x^3+3x^2+2x-3=0\)

\(\Leftrightarrow x\simeq0.67\)

b: \(\left(x+2\right)^3-\left(x-3\right)^3\)

\(=\left(x+2-x+3\right)\left[\left(x+2\right)^2+\left(x+2\right)\left(x-3\right)+\left(x-3\right)^2\right]\)

\(=5\left(x^2+4x+4+x^2-x-6+x^2-6x+9\right)\)

\(=5\left(3x^2-3x+7\right)\)