Question

Giải phương trình sau:

\(\left(x+1\right)^2+\left|x-7\right|+6=\left(x+2\right)^2\)

Answer 1

\(\left(x+1\right)^2+\left|x-7\right|+6=\left(x+2\right)^2\)

\(< =>x^2+2x+1+\left|x-7\right|+6=x^2+4x+4\)

\(< =>\left|x-7\right|=x^2-x^2+4x-2x+4-1-6\)

\(< =>\left|x-7\right|=2x-3\)

\(< =>\left[{}\begin{matrix}x-7=2x-3\\x-7=-2x+3\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x-2x=-3+7\\x+2x=3+7\end{matrix}\right.\\ < =>\left[{}\begin{matrix}-x=4\\3x=10\end{matrix}\right.\\ < =>\left[{}\begin{matrix}x=-4\\x=\dfrac{10}{3}\end{matrix}\right.\)