Question

(2x+5)²=(x+2)²

Answer 1

\(\left(2x+5\right)^2=\left(x+2\right)^2\)

\(\Leftrightarrow\left(2x+5\right)^2-\left(x+2\right)^2=0\)

\(\Leftrightarrow\left[\left(2x+5\right)-\left(x+2\right)\right]\left[\left(2x+5\right)+\left(x+2\right)\right]=0\)

\(\Leftrightarrow\left[{}\begin{matrix}\left(2x+5\right)-\left(x+2\right)=0\\\left(2x+5\right)+\left(x+2\right)=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x+5-x-2=0\\2x+5+x+2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x+3=0\\3x+7=0\end{matrix}\right.\)

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

 

Answer 2

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