\(a,x^2-16=0\)
\(\Rightarrow x^2-4^2=0\)
\(\Rightarrow\left(x-4\right)\left(x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-4=0\\x+4=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=4\\x=-4\end{matrix}\right.\)
Vậy \(x\in\left\{4;-4\right\}\)
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\(b,x^2-x+x-1=0\)
\(\Rightarrow x^2-1^2=0\)
\(\Rightarrow\left(x-1\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-1=0\\x+1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=1\\x=-1\end{matrix}\right.\)
Vậy \(x\in\left\{1;-1\right\}\)
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\(c,x^2-10x=-25\)
\(\Rightarrow x^2+10x+5^2=0\)
\(\Rightarrow\left(x+5\right)^2=0\)
\(\Rightarrow x+5=0\)
Vậy \(x=-5\)
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\(d,x^2-6x+1=8\)
\(\Rightarrow x^2-6x+1-8=0\)
\(\Rightarrow x^2-6x+3^2-9-7=0\)
\(\Rightarrow\left(x-3\right)^2-16=0\)
\(\Rightarrow\left(x-3\right)^2-4^2=0\)
\(\Rightarrow\left(x-3-4\right)\left(x-3+4\right)=0\)
\(\Rightarrow\left(x-7\right)\left(x+1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x-7=0\\x+1=0\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=7\\x=-1\end{matrix}\right.\)
Vậy \(x\in\left\{7;-1\right\}\)
a) \(x^2-16=0\\ \Leftrightarrow x^2=16\\\Leftrightarrow x=\pm16\)
b) \(x^2-x+x-1=0\\ \Leftrightarrow x^2-1=0\\ \Leftrightarrow x^2=1\\ \Leftrightarrow x=\pm1\)
c) \(x^2-10x=-25\\ \Leftrightarrow x\left(x-10\right)=-25\\ \Leftrightarrow\left[{}\begin{matrix}x=-25\\x-10=-25\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-25\\x=-15\end{matrix}\right.\)
d) \(x^2-6x+1=8\\ \Leftrightarrow x^2-6x=7\\ \Leftrightarrow x\left(x-6\right)=7\\ \Leftrightarrow\left[{}\begin{matrix}x=7\\x-6=7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=7\\x=13\end{matrix}\right.\)