Bài giải
a, \(1075\cdot\left(x-3\right)\cdot\left(x-1\right)=0\)
\(\left(x-3\right)\left(x-1\right)=0\)
\(\Rightarrow\orbr{\begin{cases}x-3=0\\x-1=0\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=3\\x=1\end{cases}}\)
\(\Rightarrow\text{ }x\in\left\{3\text{ ; }1\right\}\)
b, \(2\cdot\left(x-7\right)+3\cdot\left(x+1\right)\)
\(=2x-14+3x+3\)
\(=5x-11\)
c, \(x+1+x+2+...+x+100=5750\)
\(\left(x+x+...+x\right)+\left(1+2+...+100\right)=5750\)
\(100x+\left(100-1+1\right)\cdot\left(100+1\right)\text{ : }2=5750\)
\(100x+100\cdot101\text{ : }5=5750\)
\(100x+50\cdot101=5750\)
\(100x+5050=5750\)
\(100x=5750-5050\)
\(100x=700\)
\(x=700\text{ : }100\)
\(x=7\)
