Question

Tìm GTNN của  B= 2x^2 -x + 2017

 

Answer 1

=2(x^2 -2x1/4 +1/16)-1/8 +2017

=2(x-1/4)^2 +16135/8

MinB=16135/8 khi x =1/4

Answer 2

Ta có: \(B=2x^2-x+2017\)

\(=2\left(x^2-\dfrac{1}{2}x+\dfrac{2017}{2}\right)\)

\(=2\left(x^2-2\cdot x\cdot\dfrac{1}{4}+\dfrac{1}{16}+\dfrac{16135}{16}\right)\)

\(=2\left(x-\dfrac{1}{4}\right)^2+\dfrac{16135}{8}\ge\dfrac{16135}{8}\forall x\)

Dấu '=' xảy ra khi \(x=\dfrac{1}{4}\)