\(\left(x-3\right)^2-2.\left(x-1\right)=x.\left(x-2\right)^2-5x^2\)
\(\Leftrightarrow\left(x-3\right)^2-2.\left(x-1\right)-x.\left(x-2\right)^2+5x^2=0\)
\(\Leftrightarrow x^3-3.x^2.3+3.x.3^2-3^3-\left(2x-2\right)-x.\left(x^2-4x+4\right)+5x^2=0\)
\(\Leftrightarrow x^3-9x^2+27x-27-2x+2-\left(x^3-4x^2+4x\right)+5x^2=0\)
\(\Leftrightarrow x^3-9x^2+27x-27-2x+2-x^3+4x^2-4x+5x^2=0\)
\(\Leftrightarrow21x-25=0\)
\(\Leftrightarrow21x=0+25\)
\(\Leftrightarrow21x=25\)
\(\Leftrightarrow x=25:21\)
\(\Leftrightarrow x=\frac{25}{21}.\)
Vậy phương trình có tập hợp nghiệm là: \(S=\left\{\frac{25}{21}\right\}.\)
Chúc bạn học tốt!
