Question

Tìm x biết

(x+3)²-(x-2)(x+3)+(2x+1)³=6x(2x+1)+(2x-3)(4x²+6x+9)

Answer 1

x=\(-\frac{43}{5}\)

Answer 2

Ta có: \(\left(x+3\right)^2-\left(x-2\right)\left(x+3\right)+\left(2x+1\right)^3=6x\left(2x+1\right)+\left(2x-3\right)\left(4x^2+6x+9\right)\)\(\Leftrightarrow\left(x+3\right)\left(x+3-x+2\right)+\left(2x\right)^3+12x^2+6x+1=12x^2+6x+8x^3-27\)

\(\Leftrightarrow5\left(x+3\right)+8x^3+12x^2+6x+1=8x^3+12x^2+6x-27\)

\(\Leftrightarrow5x+15+8x^3+12x^2+6x+1=8x^3+12x^2+6x-27\)

\(\Leftrightarrow8x^3+12x^2+11x+16=8x^3+12x^2+6x-27\)

\(\Leftrightarrow5x+43=0\)

\(\Leftrightarrow5x=-43\)\(\Leftrightarrow x=\frac{-43}{5}\)

Vậy \(x=-\frac{43}{5}\)