TH1: x=0
=>\(x^2=0\)
=>M=0
TH2: x<>0
\(x^4+x^2+1\)
\(=x^4+2x^2+1-x^2\)
\(=\left(x^2+1\right)^2-x^2=\left(x^2-x+1\right)\left(x^2+x+1\right)\)
\(\frac{x}{x^2-x+1}=a\)
=>\(\frac{x^2-x+1}{x}=\frac{1}{a}\)
\(\frac{x}{x^2+x+1}=1:\frac{x^2+x+1}{x}=1:\left(\frac{x^2-x+1}{x}+\frac{2x}{x}\right)\)
\(=1:\left(\frac{1}{a}+2\right)=1:\frac{1+2a}{a}=\frac{a}{2a+1}\)
\(M=\frac{x^2}{x^4+x^2+1}\)
\(=\frac{x}{x^2+x+1}\cdot\frac{x}{x^2-x+1}\)
\(=a\cdot\frac{a}{2a+1}=\frac{a^2}{2a+1}\)
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