Question

Answer 1

1.\(p=\dfrac{x^2}{x-2}.\left(\dfrac{x^2+4}{x}-4\right)+3\)

\(=\dfrac{x^2}{x-2}.\dfrac{x^2-4x+4}{x}+3\)

\(=\dfrac{x^2}{x-2}.\dfrac{\left(x-2\right)^2}{x}+3\)

\(=x\left(x-2\right)+3=x^2-2x+3\)

2.\(P=\left(x-1\right)^2+2\\ Pmin=2\Leftrightarrow x=1\)

Answer 2

b: Ta có: \(P=x^2-2x+3\)

\(=x^2-2x+1+2\)

\(=\left(x-1\right)^2+2\ge2\forall x\)

Dấu '=' xảy ra khi x=2