a) \(x^2+10x=0\)
\(x\left(x+10\right)=0\)
\(\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)
b) \(\left(x-7\right)^3=x-7\)
\(\left(x-7\right)^3-\left(x-7\right)=0\)
\(\left(x-7\right)\left[\left(x-7\right)^2-1\right]=0\)
\(\left(x-7\right)\left(x-7-1\right)\left(x-7+1\right)=0\)
\(\left(x-7\right)\left(x-8\right)\left(x-6\right)=0\)
\(\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)
c) \(x^2-20x+100=0\)
\(x^2-10x-10x+100=0\)
\(x\left(x-10\right)-10\left(x-10\right)=0\)
\(\left(x-10\right)\left(x-10\right)=0\)
\(\left(x-10\right)^2=0\)
=> x = 10
a) \(x^2+10x=0\)
\(\Leftrightarrow x\left(x+10\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x+10=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)
Vậy..
b) \(\left(x-7\right)^3=\left(x-7\right)\)
\(\Leftrightarrow\left(x-7\right)^3-\left(x-7\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left[\left(x-7\right)^2-1\right]=0\)
\(\Leftrightarrow\left(x-7\right)\left(x-8\right)\left(x-6\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\x-8=0\\x-6=0\end{matrix}\right.\)\(\Rightarrow\left[{}\begin{matrix}x=7\\x=8\\x=6\end{matrix}\right.\)
Vậy..
c) \(x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Rightarrow x-10=0\)
\(\Rightarrow x=10\)
a, \(x^2+10x=0\)
\(\Leftrightarrow x\left(x+10\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)
Vậy x = 0 hoặc x = -10
b, \(\left(x-7\right)^3=\left(x-7\right)\)
\(\Leftrightarrow\left(x-7\right)^3-\left(x-7\right)=0\)
\(\Leftrightarrow\left(x-7\right)\left[\left(x-7\right)^2-1\right]=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=0\\\left(x-7\right)^2-1=0\end{matrix}\right.\)
+) \(x-7=0\Leftrightarrow x=7\)
+) \(\left(x-7\right)^2-1=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-7=1\\x-7=-1\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=8\\x=6\end{matrix}\right.\)
Vậy x = 7 hoặc x = 8 hoặc x = 6
c, \(x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Leftrightarrow x=10\)
Vậy x = 10
a) \(x^2+10x=0\)
\(\Leftrightarrow x\cdot\left(x+10\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x+10=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=-10\end{matrix}\right.\)
Vậy \(S=\left\{-10;0\right\}\)
b) \(\left(x-7\right)^3=\left(x-7\right)\)
Để \(\left(x-7\right)^3=\left(x-7\right)\)
\(\Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^3=0\\x-7=0\end{matrix}\right.\Leftrightarrow x=7\left(TM\right)\)
và \(\Leftrightarrow\left[{}\begin{matrix}\left(x-7\right)^3=1\\x-7=1\end{matrix}\right.\Leftrightarrow x=8\left(TM\right)\)
Vậy \(S=\left\{7;8\right\}\)
c) \(x^2-20x+100=0\)
\(\Leftrightarrow\left(x-10\right)^2=0\)
\(\Rightarrow x=10\)
Vậy \(S=\left\{10\right\}\)
