Question

Giải phương trình sau

\(\left(x-2\right)\left(x+2\right)-\left(2x+1\right)^2=x\cdot\left(2-3x\right)\)

Answer 1

\(\left(x^2-4\right)-\left(4x^2+4x+1\right)-2x+3x^2=0\)

\(\Leftrightarrow\left(x^2+3x^2-4x^2\right)+\left(-4x-2x\right)+\left(-4-1\right)=0\)

\(\Leftrightarrow-6x-5=0\Leftrightarrow x=-\frac{5}{6}\)

Vậy nghiệm phương trình là \(x=-\frac{5}{6}\)

Answer 2

\(\left(x-2\right)\left(x+2\right)-\left(2x+1\right)^2=x\left(2-3x\right)\)

\(\Leftrightarrow x^2-4-\left(4x^2+4x+1\right)=2x-3x^2\)

\(\Leftrightarrow x^2-4-4x^2-4x-1-2x+3x^2=0\)

\(\Leftrightarrow-5-6x=0\)

\(\Leftrightarrow-6x=5\Leftrightarrow x=\frac{-5}{6}\)