Question

|3-x| + (x+1)(x+5)=X2 -2

giúp e vs ạ mai e thi rồi

 

Answer 1

\(\left|3-x\right|+\left(x+1\right)\left(x+5\right)=x^2-2\)

\(\Leftrightarrow\left|3-x\right|+x^2+6x+5=x^2-2\)

\(\Leftrightarrow\left|3-x\right|=x^2-2-x^2-6x-5\)

\(\Leftrightarrow\left|3-x\right|=-6x-7\) (*)

-ĐKXĐ: \(x\le-\dfrac{7}{6}\)

(*) \(\Leftrightarrow\left[{}\begin{matrix}3-x=-6x-7\\3-x=6x+7\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}-x+6x=-7-3\\-x-6x=7-3\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}5x=-10\\-7x=4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=-2\left(nhận\right)\\x=\dfrac{-4}{7}\left(loại\right)\end{matrix}\right.\)

-Vậy \(S=\left\{-2\right\}\)