Tìm GTNN của \(D = {x^4} - 2{x^3} + 3{x^2} - 2x + 1\).

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

\(D = {\left( {{x^2} - x} \right)^2} + 2\left( {{x^2} - x} \right) + 1 = {\left( {{x^2} - x + 1} \right)^2}\)

\(D = {\left[ {{{\left( {x - \frac{1}{2}} \right)}^2} + \frac{3}{4}} \right]^2}\)

\({\left( {x - \frac{1}{2}} \right)^2} \ge 0\forall x \in R \Rightarrow {\left( {x - \frac{1}{2}} \right)^2} + \frac{3}{4} \ge \frac{3}{4}\)

\( \Rightarrow D \ge {\left( {\frac{3}{4}} \right)^2} = \frac{9}{{16}}\).