Question

Giai phuong trinh;

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

Answer 1

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

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

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

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

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

\(\Leftrightarrow\left[{}\begin{matrix}x^2+2x-1=x+3\\x^2+2x-1=-x-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x^2+x-4=0\\x^2+3x+2=0\end{matrix}\right.\)

.........giải từng phương trình ra theo công thức\(\Delta\)

=> nghiệm của phương trình..........