\(P=\frac{3x\left(x-2\right)+x^2-x+3}{x-2}\)
\(P=\frac{3x^2-6x+x^2-x+3}{x-2}\)
\(P=\frac{4x^2-7x+3}{x-2}\)
\(P\left(x-2\right)=4x^2-7x+3\)
\(Px-2P=4x^2-7x+3\)
\(4x^2-x\left(7+P\right)+3+2P=0\)
Ta có : \(\Delta=\left(7+P\right)^2-4.4\left(3+2P\right)\)
\(\Delta=7^2+14P+P^2-48-32P\)
\(\Delta=P^2-18P+1\ge0\)
\(\left\{{}\begin{matrix}x\le9-4\sqrt{2}\\x\ge9+4\sqrt{2}\end{matrix}\right.\)
Vậy \(P_{min}=9+4\sqrt{2}\)
bạn sửa lại ở dưới x là P nhé
