1. \(\left(x+1\right)^2-4=0\Leftrightarrow\left(x+1\right)^2=4\)\(\Leftrightarrow\left[{}\begin{matrix}x+1=2\\x+1=-2\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-3\end{matrix}\right.\)
2. \(9x^2-16\left(x-1\right)^2=0\Leftrightarrow9x^2=16\left(x-1\right)^2\) \(\Leftrightarrow\left[{}\begin{matrix}3x=4\left(x-1\right)\\-3x=4\left(x-1\right)\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=4\\x=\dfrac{4}{7}\end{matrix}\right.\)
3. \(x^3-3x^2+3x-1=0\Leftrightarrow x=1\)
4. \(x^3+3x^2+3x+1=0\Leftrightarrow x=-1\)
1) \(\left(x+1\right)^2-4=0\)
\(\left(x+1\right)^2=4\)
\(\left(x+1\right)^2=2^2\) hoặc \(\left(x+1\right)^2=\left(-2\right)^2\)
\(x+1=2\) hoặc \(x+1=-2\)
*) \(x+1=2\)
\(x=2-1\)
\(x=1\)
*) \(x+1=-2\)
\(x=-2-1\)
\(x=-3\)
Vậy \(x=-3;x=1\)
2) \(9x^2-16\left(x-1\right)^2=0\)
\(\left(3x\right)^2-\left(4x-4\right)^2=0\)
\(\left(3x-4x+4\right)\left(3x+4x-4\right)=0\)
\(\left(-x+4\right)\left(7x-4\right)=0\)
\(-x+4=0\) hoặc \(7x-4=0\)
*) \(-x+4=0\)
\(-x=-4\)
\(x=4\)
*) \(7x-4=0\)
\(7x=4\)
\(x=\dfrac{4}{7}\)
Vậy \(x=\dfrac{4}{7};x=4\)
3) \(x^3-3x^2+3x-1=0\)
\(\left(x-1\right)^3=0\)
\(x-1=0\)
\(x=1\)
4) \(x^3+3x^2+3x+1=0\)
\(\left(x+1\right)^3=0\)
\(x+1=0\)
\(x=-1\)
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