Ta có : \(P=\frac{x^4+2x^2+2}{x^2+1}\)
=> \(P=\frac{x^4+2x^2+1+1}{x^2+1}=\frac{\left(x^2+1\right)^2+1}{x^2+1}\)
=> \(P=x^2+1+\frac{1}{x^2+1}\)
Ta thấy : \(x^2\ge0\)
=> \(x^2+1\ge1\)
=> \(\frac{1}{x^2+1}\ge1\)
=> \(x^2+1+\frac{1}{x^2+1}\ge2\forall x\)
Vậy MinP = 2 <=> x = 0 .