\(x^4-2x^3+4x-4=0\)
\(\Leftrightarrow x^4-2x^2-2x^3+4x+2x^2-4=0\)
\(\Leftrightarrow x^2.\left(x^2-2\right)-2x.\left(x^2-2\right)+2.\left(x^2-2\right)\)
\(\Leftrightarrow\left(x^2-2\right)\left(x^2-2x+2\right)=0\)
\(\text{Mà }x^2-2x+2=x^2-2x+1+1\)
\(=\left(x-1\right)^2+1>0\text{ với mọi x }\left(\text{vì }\left(x-1\right)^2\ge0\right)\text{ nên :}\)
\(x^2-2=0\)
\(\Leftrightarrow x^2=2\)
\(\Leftrightarrow x=\sqrt{2}\text{hoặc }x=-\sqrt{2}\)
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