1: \(\Leftrightarrow x^4-5x^2+4=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x^2-1\right)=0\)
hay \(x\in\left\{1;-1;2;-2\right\}\)
2: \(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2-3x+9+x-9\right)=0\)
\(\Leftrightarrow x\left(x+3\right)\left(x-2\right)=0\)
hay \(x\in\left\{0;-3;2\right\}\)
3: \(\Leftrightarrow25\left(2x-1\right)^2-4\left(x-2\right)^2=0\)
\(\Leftrightarrow\left(10x-5\right)^2-\left(2x-4\right)^2=0\)
\(\Leftrightarrow\left(10x-5-2x+4\right)\left(10x-5+2x-4\right)=0\)
\(\Leftrightarrow\left(8x-1\right)\left(12x-9\right)=0\)
hay \(x\in\left\{\dfrac{1}{9};\dfrac{3}{4}\right\}\)
1. \(\Leftrightarrow x^4-5x^2+4=0\)
\(\Leftrightarrow x^4-4x^2-x^2+4=0\)
\(\Leftrightarrow x^2\left(x^2-4\right)-\left(x^2-4\right)=0\)
\(\Leftrightarrow\left(x^2-4\right)\left(x^2-1\right)=0\)
\(\Leftrightarrow\left(x-2\right)\left(x+2\right)\left(x-1\right)\left(x+1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\pm2\\x=\pm1\end{matrix}\right.\)
Vậy \(S=\left\{\pm2,\pm1\right\}\).
2. \(\Leftrightarrow\left(x+3\right)\left(x^2+3x+9\right)+\left(x+3\right)\left(x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2+3x+9+x-9\right)=0\)
\(\Leftrightarrow\left(x+3\right)\left(x^2+4x\right)=0\)
\(\Leftrightarrow\left(x+3\right)x\left(x+4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-3\\x=-4\\x=0\end{matrix}\right.\)
Vậy \(S=\left\{-3;-4;0\right\}\)
3) \(\Leftrightarrow4\left(x-2\right)^2-25\left(1-2x\right)^2=0\)
\(\Leftrightarrow\left[2\left(x-2\right)+5\left(1-2x\right)\right]\left[2\left(x-2\right)-5\left(1-2x\right)\right]=0\)
\(\Leftrightarrow\left(-8x+1\right)\left(12x-9\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{8}\\x=\dfrac{3}{4}\end{matrix}\right.\)
Vậy \(S=\left\{\dfrac{1}{8};\dfrac{3}{4}\right\}\)
