(2x+5)(3x-7)=(2x-5)(2x+5)
(2x+5)(3x-7-2x+5) = 0
2x-5=0 hoặc x-2=0
=> x=5/2 => x = 2
Ta có :
\(\left(2x-5\right)\left(3x+7\right)=4x^2-25\)
\(\Leftrightarrow\)\(\left(2x-5\right)\left(3x+7\right)=\left(2x\right)^2-5^2\)
\(\Leftrightarrow\)\(\left(2x-5\right)\left(3x+7\right)=\left(2x-5\right)\left(2x+5\right)\) ( VP áp dụng hằng đẳng thức \(a^2-b^2=\left(a-b\right)\left(a+b\right)\))
\(\Leftrightarrow\)\(\left(2x-5\right)\left(3x+7\right)-\left(2x-5\right)\left(2x+5\right)=0\) ( chuyển vế )
\(\Leftrightarrow\)\(\left(2x-5\right)\left(3x+7-2x-5\right)=0\) ( đặt nhân tử chung )
\(\Leftrightarrow\)\(\left(2x-5\right)\left(x+2\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-5=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}2x=0+5\\x=0-2\end{cases}}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x=5\\x=-2\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=-2\end{cases}}}\)
Vậy \(x=\frac{5}{2}\) hoặc \(x=-2\)
Chúc bạn học tốt ~
\(\left(2x-5\right)\left(3x+7\right)=4x^2-25\)
\(\Leftrightarrow\left(2x-5\right)\left(3x+7\right)=\left(2x+5\right)\left(2x-5\right)\)
\(\Leftrightarrow\left(2x-5\right)\left(3x+7\right)-\left(2x+5\right)\left(2x-5\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(3x+7-2x-5\right)=0\)
\(\Leftrightarrow\left(2x-5\right)\left(x+2\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}2x-5=0\\x+2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{5}{2}\\x=-2\end{cases}}}\)
Vậy \(S=\left\{\frac{5}{2};-2\right\}\)
