*) \(4x^2-1=0\)
\(\Rightarrow4x^2=1\Rightarrow x^2=\dfrac{1}{4}\Rightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
*) \(2x^2+0,82=1\)
\(\Rightarrow2x^2=1-0,82=\dfrac{9}{50}\)
\(\Rightarrow x^2=\dfrac{9}{100}\Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{10}\\x=-\dfrac{3}{10}\end{matrix}\right.\)
*) \(\left(3x-\dfrac{1}{4}\right)\left(x+\dfrac{1}{2}\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}3x-\dfrac{1}{4}=0\\x+\dfrac{1}{2}=0\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}3x=\dfrac{1}{4}\Rightarrow x=\dfrac{1}{12}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
Giải:
a) \(4x^2-1=0\)
\(\Leftrightarrow\left(2x\right)^2-1^2=0\)
\(\Leftrightarrow\left(2x-1\right)\left(2x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\2x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
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b) \(2x^2+0,82=1\)
\(\Leftrightarrow2x^2=0,18\)
\(\Leftrightarrow x^2=0,09\)
\(\Leftrightarrow x=\pm0,3\)
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c) \(\left(3x-\dfrac{1}{4}\right)\left(x+\dfrac{1}{2}\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-\dfrac{1}{4}=0\\x+\dfrac{1}{2}=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{12}\\x=-\dfrac{1}{2}\end{matrix}\right.\)
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