Question

Tìm GTNN của biểu thức 

a,2x^2+3x+4

Answer 1

\(2x^2+3x+4\)

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

\(=2\left(x^2+2.x.\frac{3}{4}+\frac{9}{16}+\frac{23}{16}\right)\)

\(=2\left(\left(x+\frac{3}{4}\right)^2+\frac{23}{16}\right)\)

\(=\frac{23}{8}+2\left(x+\frac{3}{4}\right)^2\ge\frac{23}{8}\)

MIN  = \(\frac{23}{8}< =>x+\frac{3}{4}=0\)

\(=>x=\frac{-3}{4}\)