Giải phương trình \(\dfrac{\left(x+2\right)^2}{4}+\dfrac{\left(x-1\right)^2}{3}=\dfrac{\left(x+1\right)\left(x-1\right)}{2}+\dfrac{x\left(x+2\right)}{6}\), ta được kết quả là
\(x=\pm\sqrt{22}\). \(x_1=\dfrac{1}{2},x_2=\dfrac{2}{3}\). \(x_1=3,x_2=4\). \(x_1=-\dfrac{6}{7},x_2=-\dfrac{4}{5}\). Hướng dẫn giải:\(\dfrac{\left(x+2\right)^2}{4}+\dfrac{\left(x-1\right)^2}{3}=\dfrac{\left(x+1\right)\left(x-1\right)}{2}+\dfrac{x\left(x+2\right)}{6}\)
\(\Leftrightarrow3.\left(x+2\right)^2+4.\left(x-1\right)^2=6\left(x+1\right)\left(x-1\right)+2x\left(x+2\right)\)
\(\Leftrightarrow3\left(x^2+4x+4\right)+4\left(x^2-2x+1\right)=6\left(x^2-1\right)+2x^2+4x\)
\(\Leftrightarrow x^2\left(3+4-6-2\right)+x\left(12-8-4\right)+12+4+6=0\)
\(\Leftrightarrow-x^2+22=0\)
\(\Leftrightarrow x=\pm\sqrt{22}\).
