Question

tim gtnn cua da thuc P=(x-1)(2x+3)

Answer 1

Ta có :

     \(P=\left(x-1\right)\left(2x+3\right)=2x^2-2x+3x-3\)      \(=2x^2+x-3\)

                                        \(=2\left(x^2+\frac{1}{2}x-\frac{3}{2}\right)\) \(=2\left(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{1}{16}-\frac{3}{2}\right)\)

                                          \(=2\left(x^2+\frac{1}{2}x+\frac{1}{16}-\frac{23}{16}\right)\)

                                           \(=2\left(x+\frac{1}{4}\right)^2-\frac{23}{8}\ge-\frac{23}{8},\)với mọi x

Vậy \(MIN_P=\frac{-23}{8}\) khi \(x+\frac{1}{4}=0\Leftrightarrow x=\frac{-1}{4}\)