1, 2x\(^2\) -8=0
2x\(^2\) =8
x\(^2\) =4 \(\Rightarrow\) \(\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
2, 3x\(^2\) -75=0
3x\(^2\) = 75
x\(^2\) = 25 \(\Rightarrow\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
3, (x+3)\(^2\) =4
\(\Rightarrow\left[{}\begin{matrix}x+3=2\\x+3=-2\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=-1\\x=-5\end{matrix}\right.\)
4, (x-1)\(^2\)-81=0
(x-1)\(^2\) =81 \(\Rightarrow\left[{}\begin{matrix}x-1=9\\x-1=-9\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}x=10\\x=-8\end{matrix}\right.\)
5, x\(^2\) +4x-21=0
x(x+4)=21
\(\Rightarrow\) \(\left\{{}\begin{matrix}x=3\\x+4=7\end{matrix}\right.\) \(\Rightarrow x=3\)
6, x\(^3\) =25x
x(x\(^2\) - 5\(^2\) )=0
x(x-5)(x+5)=0
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x+5=0\\x-5=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=0\\x=-5\\x=5\end{matrix}\right.\)
8, x\(^3\) - 49x=0
x(x-7)(x+7)=0
\(\Rightarrow\left\{{}\begin{matrix}x=0\\x-7=0\\x+7=0\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}x=0\\x=7\\x=-7\end{matrix}\right.\)
1)
\(2x^2-8=0\\ \Leftrightarrow2\left(x^2-4\right)=0\\ \Leftrightarrow2\left(x-2\right)\left(x+2\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+2=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-2\end{matrix}\right.\)
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2)
\(3x^2-75=0\\\Leftrightarrow 3\left(x^2-25\right)=0\\ \Leftrightarrow3\left(x-5\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-5=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-5\end{matrix}\right.\)
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3)
\(\left(x+3\right)^2=4\\ \Leftrightarrow\left(x+3\right)^2-4=0\\ \Leftrightarrow\left(x+3-2\right)\left(x+3+2\right)=0\\\Leftrightarrow \left(x+1\right)\left(x+5\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x+1=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-1\\x=-5\end{matrix}\right.\)
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4)
\(\left(x-1\right)^2-81=0\\ \Leftrightarrow\left(x-1-9\right)\left(x-1+9\right)=0\\\Leftrightarrow \left(x-10\right)\left(x+8\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-10=0\\x+8=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=10\\x=-8\end{matrix}\right.\)
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5)
\(x^2+7x-3x-21=0\\ \Leftrightarrow x\left(x-3\right)+7\left(x-3\right)=0\\ \Leftrightarrow\left(x-3\right)\left(x+7\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}x-3=0\\x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=3\\x=-7\end{matrix}\right.\)
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6)
\(x^3=25x\\ \Leftrightarrow x^3-25x=0\\ \Leftrightarrow x\left(x^2-5\right)=0\\ \Leftrightarrow x\left(x+5\right)\left(x-5\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x-5=0\\x+5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)
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Cầu vồng có bảy màu vì có bảy anh bangtan
