\(x.\left(x-1\right).x.\left(x-1\right)=\left(x-2\right).x.x.\left(x-1\right)\left(x\in N;x>2\right)\)
\(\Rightarrow\left(x^2-x\right).\left(x^2-x\right)=\left(x-2\right).x^2.\left(x-1\right)\)
\(\Rightarrow x^4-x^3-x^3+x^2=\left(x-2\right).\left(x-1\right).x^2\)
\(\Rightarrow x^4-2x^3+x^2=\left(x^2-x-2x+2\right).x^2\)
\(\Rightarrow x^4-2x^3+x^2=x^4-x^3-2x^3+2x^2\)
\(\Rightarrow x^4-2x^3+x^2-x^4+x^3+2x^3+2x^2=0\)
\(\Rightarrow x^4-x^4+2x^3-2x^3+2x^2+x^2+x^3=0\)
\(\Rightarrow x^2.\left(2+1+x\right)=0\)
\(\Rightarrow x^2=0hoac2+1+x=0\)
\(\Rightarrow x^2=0^2\) \(\Rightarrow3+x=0\)
\(\Rightarrow x=0;\Rightarrow x=-3\)
Mà \(x\in N;x>2\)
\(\Rightarrow x\in\varnothing\)
Vậy \(x\in\varnothing\)
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